1
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Duque F, Macedo CFB, Vicente R, Cardoso V. Extreme-Mass-Ratio Inspirals in Ultralight Dark Matter. PHYSICAL REVIEW LETTERS 2024; 133:121404. [PMID: 39373437 DOI: 10.1103/physrevlett.133.121404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Revised: 03/13/2024] [Accepted: 08/09/2024] [Indexed: 10/08/2024]
Abstract
Previous works have argued that future gravitational-wave detectors will be able to probe the properties of astrophysical environments where binaries coalesce, including accretion disks, but also dark matter structures. Most analyses have resorted to a Newtonian modeling of the environmental effects, which are not suited to study extreme-mass-ratio inspirals immersed in structures of ultralight bosons. In this Letter, we use relativistic perturbation theory to consistently study these systems in spherical symmetry. We compute the flux of scalar particles and the rate at which orbital energy is dissipated via gravitational radiation and depletion of scalars, i.e., dynamical friction. Our results confirm that the Laser Interferometer Space Antenna will be able to probe ultralight dark matter structures by tracking the phase of extreme-mass-ratio inspirals.
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Affiliation(s)
| | | | | | - Vitor Cardoso
- CENTRA, Departamento de Física, Instituto Superior Técnico-IST, Universidade de Lisboa-UL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal
- Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
- Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
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2
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Mougiakakos S, Vanhove P. Schwarzschild Metric from Scattering Amplitudes to All Orders in G_{N}. PHYSICAL REVIEW LETTERS 2024; 133:111601. [PMID: 39331996 DOI: 10.1103/physrevlett.133.111601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2024] [Accepted: 08/15/2024] [Indexed: 09/29/2024]
Abstract
We apply a formulation of Einstein's general relativity with only cubic interactions for deriving the metric of a Schwarzschild black hole to all orders in perturbation theory. This cubic interactions formulation coupled to effective worldline action of a massive point particle allows to derive a recursion relation for the form factors of the off-shell graviton emission current. The unique solution to the recursion relation leads to the Schwarzschild black-hole solution in four dimensions. This provides the first derivation of the black hole metric from a matter source to all orders in perturbation theory from an amplitude approach.
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3
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Bern Z, Herrmann E, Roiban R, Ruf MS, Smirnov AV, Smirnov VA, Zeng M. Conservative Binary Dynamics at Order α^{5} in Electrodynamics. PHYSICAL REVIEW LETTERS 2024; 132:251601. [PMID: 38996230 DOI: 10.1103/physrevlett.132.251601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Revised: 02/15/2024] [Accepted: 05/08/2024] [Indexed: 07/14/2024]
Abstract
We compute the potential-photon contributions to the classical relativistic scattering angle of two charged nonspinning bodies in electrodynamics through fifth order in the coupling. We use the scattering amplitudes framework, effective field theory, and multiloop integration techniques based on integration by parts and differential equations. At fifth order, the result is expressed in terms of cyclotomic polylogarithms. Our calculation demonstrates the feasibility of the corresponding calculations in general relativity, including the evaluation of the encountered four-loop integrals.
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Affiliation(s)
| | | | | | | | | | - Vladimir A Smirnov
- Moscow Center for Fundamental and Applied Mathematics, 119992 Moscow, Russia
- Skobeltsyn Institute of Nuclear Physics of Moscow State University, 119991, Moscow, Russia
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4
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Driesse M, Jakobsen GU, Mogull G, Plefka J, Sauer B, Usovitsch J. Conservative Black Hole Scattering at Fifth Post-Minkowskian and First Self-Force Order. PHYSICAL REVIEW LETTERS 2024; 132:241402. [PMID: 38949358 DOI: 10.1103/physrevlett.132.241402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2024] [Accepted: 05/13/2024] [Indexed: 07/02/2024]
Abstract
We compute the fifth post-Minkowskian (5PM) order contributions to the scattering angle and impulse of classical black hole scattering in the conservative sector at first self-force order using the worldline quantum field theory formalism. This challenging four-loop computation required the use of advanced integration-by-parts and differential equation technology implemented on high-performance computing systems. Use of partial fraction identities allowed us to render the complete integrand in a fully planar form. The resulting function space is simpler than expected: In the scattering angle, we see only multiple polylogarithms up to weight three and a total absence of the elliptic integrals that appeared at 4PM order. All checks on our result, both internal-cancellation of dimensional regularization poles and preservation of the on-shell condition-and external-matching the slow-velocity limit with the post-Newtonian (PN) literature up to 5PN order and matching the tail terms to the 4PM loss of energy-are passed.
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5
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Frellesvig H, Morales R, Wilhelm M. Calabi-Yau Meets Gravity: A Calabi-Yau Threefold at Fifth Post-Minkowskian Order. PHYSICAL REVIEW LETTERS 2024; 132:201602. [PMID: 38829078 DOI: 10.1103/physrevlett.132.201602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2024] [Accepted: 04/08/2024] [Indexed: 06/05/2024]
Abstract
We study geometries occurring in Feynman integrals that contribute to the scattering of black holes in the post-Minkowskian (PM) expansion. These geometries become relevant to gravitational-wave production from binary mergers through the classical conservative potential. At 4PM, a K3 surface is known to occur in a three-loop integral, leading to elliptic integrals in the result. In this Letter, we identify a Calabi-Yau threefold in a four-loop integral, contributing at 5PM. The presence of this Calabi-Yau geometry indicates that completely new functions occur in the full analytical results.
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Affiliation(s)
- Hjalte Frellesvig
- Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
| | - Roger Morales
- Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
- Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Matthias Wilhelm
- Niels Bohr International Academy, Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark
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6
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Bjerrum-Bohr NEJ, Chen G, Skowronek M. Covariant Compton Amplitudes in Gravity with Classical Spin. PHYSICAL REVIEW LETTERS 2024; 132:191603. [PMID: 38804943 DOI: 10.1103/physrevlett.132.191603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2023] [Revised: 03/06/2024] [Accepted: 04/11/2024] [Indexed: 05/29/2024]
Abstract
We develop a novel amplitude bootstrap technique manifestly free of unphysical poles for classically spinning particles interacting with gravitons utilizing only the double-copy and physical factorization limits. Combined with nonfactorization polynomial contact contributions from physical data for Kerr black holes, we can address high-spin-order covariant gravitational Compton amplitudes, identifying a pattern for the amplitude that we believe could extend to all orders in spin. Finally, we outline applications and outstanding questions.
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Affiliation(s)
- N Emil J Bjerrum-Bohr
- Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Gang Chen
- Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Marcos Skowronek
- Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
- Department of Physics, Brown University, Providence, Rhode Island 02912, USA
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7
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Witzany V, Piovano GA. Analytic Solutions for the Motion of Spinning Particles near Spherically Symmetric Black Holes and Exotic Compact Objects. PHYSICAL REVIEW LETTERS 2024; 132:171401. [PMID: 38728722 DOI: 10.1103/physrevlett.132.171401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Revised: 01/15/2024] [Accepted: 03/26/2024] [Indexed: 05/12/2024]
Abstract
Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured in the motion of a spinning test particle. We solve the equations motion of a spinning particle to leading order in spin in arbitrary static and spherically symmetric space-times in terms of one-dimensional closed-form integrals. This solves the problem and proves its integrability in a wide range of modified gravities and near exotic compact objects. Then, by specializing to the case of bound orbits in Schwarzschild space-time, we demonstrate how to express the solution in the form of Jacobi elliptic functions.
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Affiliation(s)
- Vojtěch Witzany
- Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, CZ-180 00 Prague, Czech Republic
| | - Gabriel Andres Piovano
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
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8
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Jakobsen GU. Spin and Susceptibility Effects of Electromagnetic Self-Force in Effective Field Theory. PHYSICAL REVIEW LETTERS 2024; 132:151601. [PMID: 38682993 DOI: 10.1103/physrevlett.132.151601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Revised: 02/06/2024] [Accepted: 03/20/2024] [Indexed: 05/01/2024]
Abstract
The classic Abraham-Lorentz-Dirac self-force of pointlike particles is generalized within an effective field theory setup to include linear spin and susceptibility effects described perturbatively, in that setup, by effective couplings in the action. Electromagnetic self-interactions of the pointlike particle are integrated out using the in-in supersymmetric worldline quantum field theory formalism. Divergences are regularized with dimensional regularization, and the resulting equations of motion are in terms only of an external electromagnetic field and the particle degrees of freedom.
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Affiliation(s)
- Gustav Uhre Jakobsen
- Institut für Physik und IRIS Adlershof, Humboldt Universität zu Berlin, Zum Großen Windkanal 2, 12489 Berlin, Germany and Max Planck Institut für Gravitationsphysik (Albert Einstein Institut), Am Mühlenberg 1, 14476 Potsdam, Germany
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9
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Taujanskas G, Valiente Kroon JA. At the interface of asymptotics, conformal methods and analysis in general relativity. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2024; 382:20230048. [PMID: 38219787 PMCID: PMC10788158 DOI: 10.1098/rsta.2023.0048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Accepted: 12/11/2023] [Indexed: 01/16/2024]
Abstract
This is an introductory article for the proceedings associated with the Royal Society Hooke discussion meeting of the same title which took place in London in May 2023. We review the history of Penrose's conformal compactification, null infinity and a number of related fundamental developments in mathematical general relativity from the last 60 years. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.
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Affiliation(s)
- G. Taujanskas
- Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, CB3 0WB, UK
| | - J. A. Valiente Kroon
- School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK
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10
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Panosso Macedo R. Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2024; 382:20230046. [PMID: 38219779 DOI: 10.1098/rsta.2023.0046] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 10/31/2023] [Indexed: 01/16/2024]
Abstract
This work offers a didactical introduction to the calculations and geometrical properties of a static, spherically symmetric spacetime foliated by hyperboloidal time surfaces. We discuss the various degrees of freedom involved, namely the height function, responsible for introducing the hyperboloidal time coordinate, and a radial compactification function. A central outcome is the expression of the Trautman-Bondi mass in terms of the hyperboloidal metric functions. Moreover, we apply this formalism to a class of wave equations commonly used in black-hole perturbation theory. Additionally, we provide a comprehensive derivation of the hyperboloidal minimal gauge, introducing two alternative approaches within this conceptual framework: the in-out and out-in strategies. Specifically, we demonstrate that the height function in the in-out strategy follows from the well-known tortoise coordinate by changing the sign of the terms that become singular at future null infinity. Similarly, for the out-in strategy, a sign change also occurs in the tortoise coordinate's regular terms. We apply the methodology to the following spacetimes: Singularity-approaching slices in Schwarzschild, higher-dimensional black holes, black hole with matter halo, and Reissner-Nordström-de Sitter. From this heuristic study, we conjecture that the out-in strategy is best adapted for black hole geometries that account for environmental or effective quantum effects. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'.
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Affiliation(s)
- Rodrigo Panosso Macedo
- Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, Copenhagen 2100, Denmark
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11
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Cheung C, Parra-Martinez J, Rothstein IZ, Shah N, Wilson-Gerow J. Effective Field Theory for Extreme Mass Ratio Binaries. PHYSICAL REVIEW LETTERS 2024; 132:091402. [PMID: 38489645 DOI: 10.1103/physrevlett.132.091402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2023] [Accepted: 01/23/2024] [Indexed: 03/17/2024]
Abstract
We derive an effective field theory describing a pair of gravitationally interacting point particles in an expansion in their mass ratio, also known as the self-force (SF) expansion. The 0SF dynamics are trivially obtained to all orders in Newton's constant by the geodesic motion of the light body in a Schwarzschild background encoding the gravitational field of the heavy body. The corrections at 1SF and higher are generated by perturbations about this configuration-that is, the geodesic deviation of the light body and the fluctuation graviton-but crucially supplemented by an operator describing the recoil of the heavy body as it interacts with the smaller companion. Using this formalism we compute new results at third post-Minkowskian order for the conservative dynamics of a system of gravitationally interacting massive particles coupled to a set of additional scalar and vector fields.
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Affiliation(s)
- Clifford Cheung
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Julio Parra-Martinez
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
- Department of Physics and Astronomy, University of British Columbia, Vancouver, V6T 1Z1, Canada
| | - Ira Z Rothstein
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Nabha Shah
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Jordan Wilson-Gerow
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
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12
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Jakobsen GU, Mogull G, Plefka J, Sauer B. Dissipative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order. PHYSICAL REVIEW LETTERS 2023; 131:241402. [PMID: 38181150 DOI: 10.1103/physrevlett.131.241402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Accepted: 11/09/2023] [Indexed: 01/07/2024]
Abstract
We compute the radiation reacted momentum impulse Δp_{i}^{μ}, spin kick ΔS_{i}^{μ}, and scattering angle θ between two scattered spinning massive bodies (black holes or neutron stars) using the N=1 supersymmetric worldline quantum field theory formalism up to fourth post-Minkowskian (4PM) order. Our calculation confirms the state-of-the-art nonspinning results, and extends them to include spin-orbit effects. Advanced multiloop Feynman integral technology including differential equations and the method of regions are applied and extended to deal with the retarded propagators arising in a causal description of the scattering dynamics. From these results we determine a complete set of radiative fluxes at subleading PM order: the 4PM radiated four-momentum and, via linear response, the 3PM radiated angular momentum, both again including spin-orbit effects.
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Affiliation(s)
- Gustav Uhre Jakobsen
- Institut für Physik und IRIS Adlershof, Humboldt Universität zu Berlin, Zum Großen Windkanal 2, 12489 Berlin, Germany
- Max Planck Institut für Gravitationsphysik (Albert Einstein Institut), Am Mühlenberg 1, 14476 Potsdam, Germany
| | - Gustav Mogull
- Institut für Physik und IRIS Adlershof, Humboldt Universität zu Berlin, Zum Großen Windkanal 2, 12489 Berlin, Germany
- Max Planck Institut für Gravitationsphysik (Albert Einstein Institut), Am Mühlenberg 1, 14476 Potsdam, Germany
| | - Jan Plefka
- Institut für Physik und IRIS Adlershof, Humboldt Universität zu Berlin, Zum Großen Windkanal 2, 12489 Berlin, Germany
| | - Benjamin Sauer
- Institut für Physik und IRIS Adlershof, Humboldt Universität zu Berlin, Zum Großen Windkanal 2, 12489 Berlin, Germany
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13
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Adamo T, Cristofoli A, Ilderton A, Klisch S. All Order Gravitational Waveforms from Scattering Amplitudes. PHYSICAL REVIEW LETTERS 2023; 131:011601. [PMID: 37478447 DOI: 10.1103/physrevlett.131.011601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Revised: 05/08/2023] [Accepted: 05/31/2023] [Indexed: 07/23/2023]
Abstract
Waveforms are classical observables associated with any radiative physical process. Using scattering amplitudes, these are usually computed in a weak-field regime to some finite order in the post-Newtonian or post-Minkowskian approximation. Here, we use strong-field amplitudes to compute the waveform produced in scattering of massive particles on gravitational plane waves, treated as exact nonlinear solutions of the vacuum Einstein equations. Notably, the waveform contains an infinite number of post-Minkowskian contributions, as well as tail effects. We also provide, and contrast with, analogous results in electromagnetism.
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Affiliation(s)
- Tim Adamo
- School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
| | - Andrea Cristofoli
- School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
| | - Anton Ilderton
- Higgs Centre, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
| | - Sonja Klisch
- School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
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14
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Wardell B, Pound A, Warburton N, Miller J, Durkan L, Le Tiec A. Gravitational Waveforms for Compact Binaries from Second-Order Self-Force Theory. PHYSICAL REVIEW LETTERS 2023; 130:241402. [PMID: 37390425 DOI: 10.1103/physrevlett.130.241402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2022] [Revised: 02/01/2023] [Accepted: 03/28/2023] [Indexed: 07/02/2023]
Abstract
We produce gravitational waveforms for nonspinning compact binaries undergoing a quasicircular inspiral. Our approach is based on a two-timescale expansion of the Einstein equations in second-order self-force theory, which allows first-principles waveform production in tens of milliseconds. Although the approach is designed for extreme mass ratios, our waveforms agree remarkably well with those from full numerical relativity, even for comparable-mass systems. Our results will be invaluable in accurately modeling extreme-mass-ratio inspirals for the LISA mission and intermediate-mass-ratio systems currently being observed by the LIGO-Virgo-KAGRA Collaboration.
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Affiliation(s)
- Barry Wardell
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, D04 V1W8, Ireland
| | - Adam Pound
- School of Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Niels Warburton
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, D04 V1W8, Ireland
| | - Jeremy Miller
- Shamoon College of Engineering, Jabotinsky 84, Ashdod, 77245, Israel
| | - Leanne Durkan
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, D04 V1W8, Ireland
| | - Alexandre Le Tiec
- Laboratoire Univers et Théories, Observatoire de Paris, CNRS, Université PSL, Université de Paris, F-92190 Meudon, France
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15
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Destounis K, Huez G, Kokkotas KD. Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickers. GENERAL RELATIVITY AND GRAVITATION 2023; 55:71. [PMID: 37283659 PMCID: PMC10239393 DOI: 10.1007/s10714-023-03119-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 05/19/2023] [Indexed: 06/08/2023]
Abstract
Due to the growing capacity of gravitational-wave astronomy and black-hole imaging, we will soon be able to emphatically decide if astrophysical dark objects lurking in galactic centers are black holes. Sgr A*, one of the most prolific astronomical radio sources in our galaxy, is the focal point for tests of general relativity. Current mass and spin constraints predict that the central object of the Milky Way is supermassive and slowly rotating, thus can be conservatively modeled as a Schwarzschild black hole. Nevertheless, the well-established presence of accretion disks and astrophysical environments around supermassive compact objects can significantly deform their geometry and complicate their observational scientific yield. Here, we study extreme-mass-ratio binaries comprised of a minuscule secondary object inspiraling onto a supermassive Zipoy-Voorhees compact object; the simplest exact solution of general relativity that describes a static, spheroidal deformation of Schwarzschild spacetime. We examine geodesics of prolate and oblate deformations for generic orbits and reevaluate the non-integrability of Zipoy-Voorhees spacetime through the existence of resonant islands in the orbital phase space. By including radiation loss with post-Newtonian techniques, we evolve stellar-mass secondary objects around a supermassive Zipoy-Voorhees primary and find clear imprints of non-integrability in these systems. The peculiar structure of the primary, allows for, not only typical single crossings of transient resonant islands, that are well-known for non-Kerr objects, but also inspirals that transverse through several islands, in a brief period of time, that lead to multiple glitches in the gravitational-wave frequency evolution of the binary. The detectability of glitches with future spaceborne detectors can, therefore, narrow down the parameter space of exotic solutions that, otherwise, can cast identical shadows with black holes.
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Affiliation(s)
- Kyriakos Destounis
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
- INFN, Sezione di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
- Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
| | - Giulia Huez
- Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
- Physics Department, University of Trento, Via Sommarive 14, 38123 Trento, Italy
| | - Kostas D. Kokkotas
- Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
- Section of Astrophysics, Astronomy, and Mechanics, Department of Physics, National and Kapodistrian University of Athens, Panepistimiopolis Zografos GR15783, Athens, Greece
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16
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Dlapa C, Kälin G, Liu Z, Neef J, Porto RA. Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order. PHYSICAL REVIEW LETTERS 2023; 130:101401. [PMID: 36962024 DOI: 10.1103/physrevlett.130.101401] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
We obtain the total impulse in the scattering of nonspinning binaries in general relativity at fourth post-Minkowskian order, i.e., O(G^{4}), including linear, nonlinear, and hereditary radiation-reaction effects. We derive the total radiated spacetime momentum as well as the associated energy flux. The latter can be used to compute gravitational-wave observables for generic (un)bound orbits. We employ the ("in-in") Schwinger-Keldysh worldline effective field theory framework in combination with modern "multiloop" integration techniques from collider physics. The complete results are in agreement with various partial calculations in the post-Minkowskian and post-Newtonian expansion.
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Affiliation(s)
- Christoph Dlapa
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - Gregor Kälin
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - Zhengwen Liu
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
- Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Jakob Neef
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, D04 V1W8, Ireland
- Humboldt-Universität zu Berlin, Zum Grossen Windkanal 2, D-12489 Berlin, Germany
| | - Rafael A Porto
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
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17
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Blanco FM, Flanagan ÉÉ. Particle Motion under the Conservative Piece of the Self-Force is Hamiltonian. PHYSICAL REVIEW LETTERS 2023; 130:051201. [PMID: 36800446 DOI: 10.1103/physrevlett.130.051201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 12/06/2022] [Indexed: 06/18/2023]
Abstract
We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic, or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian dynamics, and we derive an explicit expression for the Hamiltonian on phase space. Specialized to the Kerr spacetime, our result generalizes the Hamiltonian function previously obtained by Fujita et al. [Classical Quantum Gravity 34, 134001 (2017).CQGRDG0264-938110.1088/1361-6382/aa7342], which is valid only for nonresonant orbits.
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Affiliation(s)
| | - Éanna É Flanagan
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
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Cardoso V, Destounis K, Duque F, Macedo RP, Maselli A. Gravitational Waves from Extreme-Mass-Ratio Systems in Astrophysical Environments. PHYSICAL REVIEW LETTERS 2022; 129:241103. [PMID: 36563262 DOI: 10.1103/physrevlett.129.241103] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Revised: 11/06/2022] [Accepted: 11/21/2022] [Indexed: 06/17/2023]
Abstract
We establish a generic, fully relativistic formalism to study gravitational-wave emission by extreme-mass-ratio systems in spherically symmetric, nonvacuum black hole spacetimes. The potential applications to astrophysical setups range from black holes accreting baryonic matter to those within axionic clouds and dark matter environments, allowing one to assess the impact of the galactic potential, of accretion, gravitational drag, and halo feedback on the generation and propagation of gravitational waves. We apply our methods to a black hole within a halo of matter. We find fluid modes imparted to the gravitational-wave signal (a clear evidence of the black hole fundamental mode instability) and the tantalizing possibility to infer galactic properties from gravitational-wave measurements by sensitive, low-frequency detectors.
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Affiliation(s)
- Vitor Cardoso
- Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
- CENTRA, Departamento de Física, Instituto Superior Técnico-IST, Universidade de Lisboa-UL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal
| | - Kyriakos Destounis
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Roma, Italy
- INFN, Sezione di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy
- Theoretical Astrophysics, IAAT, University of Tübingen, 72076 Tübingen, Germany
| | - Francisco Duque
- CENTRA, Departamento de Física, Instituto Superior Técnico-IST, Universidade de Lisboa-UL, Avenida Rovisco Pais 1, 1049 Lisboa, Portugal
| | - Rodrigo Panosso Macedo
- STAG Research Centre, University of Southampton, University Road SO17 1BJ, Southampton, United Kingdom
| | - Andrea Maselli
- Gran Sasso Science Institute (GSSI), I-67100 L'Aquila, Italy
- INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy
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19
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Nagar A, Albanesi S. Toward a gravitational self-force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.064049] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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20
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Speeney N, Antonelli A, Baibhav V, Berti E. Impact of relativistic corrections on the detectability of dark-matter spikes with gravitational waves. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.044027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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21
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Battista E, De Falco V. Gravitational waves at the first post-Newtonian order with the Weyssenhoff fluid in Einstein-Cartan theory. THE EUROPEAN PHYSICAL JOURNAL. C, PARTICLES AND FIELDS 2022; 82:628. [PMID: 35891936 PMCID: PMC9307564 DOI: 10.1140/epjc/s10052-022-10558-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/15/2022] [Accepted: 06/24/2022] [Indexed: 11/18/2022]
Abstract
The generation of gravitational waves from a post-Newtonian source endowed with a quantum spin, modeled by the Weyssenhoff fluid, is investigated in the context of Einstein-Cartan theory at the first post-Newtonian level by resorting to the Blanchet-Damour formalism. After having worked out the basic principles of the hydrodynamics in Einstein-Cartan framework, we study the Weyssenhoff fluid within the post-Newtonian approximation scheme. The complexity of the underlying dynamical equations suggests to employ a discrete description via the point-particle limit, a procedure which permits the analysis of inspiralling spinning compact binaries. We then provide a first application of our results by considering binary neutron star systems.
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Affiliation(s)
- Emmanuele Battista
- Department of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Vittorio De Falco
- Scuola Superiore Meridionale, Largo San Marcellino 10, 80138 Napoli, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Napoli, Italy
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22
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Isoyama S, Fujita R, Chua AJK, Nakano H, Pound A, Sago N. Adiabatic Waveforms from Extreme-Mass-Ratio Inspirals: An Analytical Approach. PHYSICAL REVIEW LETTERS 2022; 128:231101. [PMID: 35749171 DOI: 10.1103/physrevlett.128.231101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 05/06/2022] [Indexed: 06/15/2023]
Abstract
Scientific analysis for the gravitational wave detector LISA will require theoretical waveforms from extreme-mass-ratio inspirals (EMRIs) that extensively cover all possible orbital and spin configurations around astrophysical Kerr black holes. However, on-the-fly calculations of these waveforms have not yet overcome the high dimensionality of the parameter space. To confront this challenge, we present a user-ready EMRI waveform model for generic (eccentric and inclined) orbits in Kerr spacetime, using an analytical self-force approach. Our model accurately covers all EMRIs with arbitrary inclination and black hole spin, up to modest eccentricity (≲0.3) and separation (≳2-10 M from the last stable orbit). In that regime, our waveforms are accurate at the leading "adiabatic" order, and they approximately capture transient self-force resonances that significantly impact the gravitational wave phase. The model fills an urgent need for extensive waveforms in ongoing data-analysis studies, and its individual components will continue to be useful in future science-adequate waveforms.
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Affiliation(s)
- Soichiro Isoyama
- School of Mathematics and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
- International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal-RN 59078-970, Brazil
| | - Ryuichi Fujita
- Institute of Liberal Arts, Otemon Gakuin University, Osaka 567-8502, Japan
- Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
| | - Alvin J K Chua
- Theoretical Astrophysics Group, California Institute of Technology, Pasadena, California 91125, USA
| | | | - Adam Pound
- School of Mathematics and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Norichika Sago
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
- Advanced Mathematical Institute, Osaka City University, Osaka 558-8585, Japan
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23
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Bern Z, Parra-Martinez J, Roiban R, Ruf MS, Shen CH, Solon MP, Zeng M. Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at O(G^{4}). PHYSICAL REVIEW LETTERS 2022; 128:161103. [PMID: 35522489 DOI: 10.1103/physrevlett.128.161103] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Accepted: 01/26/2022] [Indexed: 06/14/2023]
Abstract
We complete the calculation of conservative two-body scattering dynamics at fourth post-Minkowskian order, i.e., O(G^{4}) and all orders in velocity, including radiative contributions corresponding to the tail effect in general relativity. As in previous calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves complete elliptic integrals, and polylogarithms with up to transcendental weight 2. Using the amplitude-action relation, we obtain the radial action directly from the amplitude, and match the known overlapping terms in the post-Newtonian expansion.
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Affiliation(s)
- Zvi Bern
- Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Julio Parra-Martinez
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Radu Roiban
- Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Michael S Ruf
- Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Chia-Hsien Shen
- Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0319, USA
| | - Mikhail P Solon
- Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Mao Zeng
- Higgs Centre for Theoretical Physics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
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24
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Barsanti S, De Luca V, Maselli A, Pani P. Detecting Subsolar-Mass Primordial Black Holes in Extreme Mass-Ratio Inspirals with LISA and Einstein Telescope. PHYSICAL REVIEW LETTERS 2022; 128:111104. [PMID: 35363035 DOI: 10.1103/physrevlett.128.111104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Revised: 12/14/2021] [Accepted: 02/28/2022] [Indexed: 06/14/2023]
Abstract
Primordial black holes possibly formed in the early Universe could provide a significant fraction of the dark matter and would be unique probes of inflation. A smoking gun for their discovery would be the detection of a subsolar mass compact object. We argue that extreme mass-ratio inspirals will be ideal to search for subsolar-mass black holes not only with LISA but also with third-generation ground-based detectors such as Cosmic Explorer and the Einstein Telescope. These sources can provide unparalleled measurements of the mass of the secondary object at a subpercent level for primordial black holes as light as O(0.01) M_{⊙} up to luminosity distances around hundred megaparsec and few gigaparsec for LISA and Einstein Telescope, respectively, in a complementary frequency range. This would allow claiming, with very high statistical confidence, the detection of a subsolar-mass black hole, which would also provide a novel (and currently undetectable) family of sources for third-generation detectors.
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Affiliation(s)
- Susanna Barsanti
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
- INFN, Sezione di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
| | - Valerio De Luca
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
- Département de Physique Théorique and Centre for Astroparticle Physics (CAP), Université de Genève, 24 quai E. Ansermet, CH-1211 Geneva, Switzerland
| | - Andrea Maselli
- Gran Sasso Science Institute (GSSI), I-67100 L'Aquila, Italy
- INFN, Laboratori Nazionali del Gran Sasso, I-67100 Assergi, Italy
| | - Paolo Pani
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
- INFN, Sezione di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy
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26
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Multi-Messenger Astrophysics of a Millisecond Pulsar Orbiting around a Massive Black Hole. UNIVERSE 2022. [DOI: 10.3390/universe8020078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
Abstract
Extreme-mass-ratio and intermediate-mass-ratio binaries with a millisecond pulsar are gravitational-wave sources that emit also electromagnetic radiation. The millisecond pulsars in these binaries have complex orbital and spin dynamics, which are observable because of spin–orbit and spin–spin coupling (through spin–curvature interaction). The strengths of the couplings generally depends on the mass ratio between the pulsar and the black hole. The narrow mass range of neutron stars gives an advantage in parameter extraction as it greatly reduces the search space, in particular, in the determination of the black-hole mass, in gravitational wave experiments and radio pulsar timing observations. Extreme-mass-ratio and intermediate-mass-ratio binaries with a millisecond pulsar will help to resolve the astrophysical problems, concerning the applicability of the M-σ relation for galactic spheroids extending to the very low-mass galaxies and whether or not low-mass dwarf galaxies and globular clusters would harbour a nuclear intermediate-mass black hole. The high-precision that can be achieved in gravitational wave experiments and radio pulsar timing observations will provide an opportunity to directly detect gravitational clock effects that are arisen from spin couplings. Radio monitoring of the orbital and spin evolution of the millisecond pulsar in an extreme-mass-ratio binary can be used as a bootstrap method for correcting the drifts in the phases in the gravitational waves from the extreme-mass-ratio and intermediate-mass-ratio binaries caused by self-force.
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27
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Bonetto R, Pound A, Sam Z. Deformed Schwarzschild horizons in second-order perturbation theory: Mass, geometry, and teleology. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.105.024048] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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28
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Fundamental Gravity and Gravitational Waves. Symmetry (Basel) 2021. [DOI: 10.3390/sym13122384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
While being as old as general relativity itself, the gravitational two-body problem has never been under so intense investigation as it is today, spurred by both phenomenological and theoretical motivations. The observations of gravitational waves emitted by compact binary coalescences bear the imprint of the source dynamics, and as the sensitivity of detectors improve over years, more accurate modeling is being required. The analytic modeling of classical gravitational dynamics has been enriched in this century by powerful methods borrowed from field theory. Despite being originally developed in the context of fundamental particle quantum scatterings, their applications to classical, bound system problems have shown that many features usually associated with quantum field theory, such as, e.g., divergences and counterterms, renormalization group, loop expansion, and Feynman diagrams, have only to do with field theory, be it quantum or classical. The aim of this work is to present an overview of this approach, which models massive astrophysical objects as nonrelativistic particles and their gravitational interactions via classical field theory, being well aware that while the introductory material in the present article is meant to represent a solid background for newcomers in the field, the results reviewed here will soon become obsolete, as this field is undergoing rapid development.
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29
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Dhesi M, Rüter HR, Pound A, Barack L, Pfeiffer HP. Worldtube excision method for intermediate-mass-ratio inspirals: Scalar-field toy model. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.124002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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30
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Lenzi M, Sopuerta CF. Master functions and equations for perturbations of vacuum spherically symmetric spacetimes. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.084053] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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31
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Warburton N, Pound A, Wardell B, Miller J, Durkan L. Gravitational-Wave Energy Flux for Compact Binaries through Second Order in the Mass Ratio. PHYSICAL REVIEW LETTERS 2021; 127:151102. [PMID: 34678035 DOI: 10.1103/physrevlett.127.151102] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 09/07/2021] [Indexed: 06/13/2023]
Abstract
Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are consistent with post-Newtonian calculations in the weak field, and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modeling extreme-mass-ratio inspirals and will be useful in modeling intermediate-mass-ratio systems.
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Affiliation(s)
- Niels Warburton
- School of Mathematics and Statistics, University College Dublin, Belfield D04 V1W8, Dublin 4, Ireland
| | - Adam Pound
- School of Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Barry Wardell
- School of Mathematics and Statistics, University College Dublin, Belfield D04 V1W8, Dublin 4, Ireland
| | - Jeremy Miller
- Department of Physics, Ariel University, Ariel 40700, Israel
| | - Leanne Durkan
- School of Mathematics and Statistics, University College Dublin, Belfield D04 V1W8, Dublin 4, Ireland
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32
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Destounis K, Kokkotas KD. Gravitational-wave glitches: Resonant islands and frequency jumps in nonintegrable extreme-mass-ratio inspirals. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.064023] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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33
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Albanesi S, Nagar A, Bernuzzi S. Effective one-body model for extreme-mass-ratio spinning binaries on eccentric equatorial orbits: Testing radiation reaction and waveform. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.104.024067] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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34
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O’Toole C, Ottewill A, Wardell B. Characteristic formulation of the Regge-Wheeler and Zerilli Green functions. Int J Clin Exp Med 2021. [DOI: 10.1103/physrevd.103.124022] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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35
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36
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Bern Z, Parra-Martinez J, Roiban R, Ruf MS, Shen CH, Solon MP, Zeng M. Scattering Amplitudes and Conservative Binary Dynamics at O(G^{4}). PHYSICAL REVIEW LETTERS 2021; 126:171601. [PMID: 33988437 DOI: 10.1103/physrevlett.126.171601] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 03/11/2021] [Indexed: 06/12/2023]
Abstract
Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G^{4}). As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at O(G^{3}) via its relation to the tail effect.
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Affiliation(s)
- Zvi Bern
- Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Julio Parra-Martinez
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Radu Roiban
- Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Michael S Ruf
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Chia-Hsien Shen
- Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0319, USA
| | - Mikhail P Solon
- Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Mao Zeng
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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37
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Interpretations and Naturalness in the Radiation-Reaction Problem. Symmetry (Basel) 2021. [DOI: 10.3390/sym13040658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
After more than a century of history, the radiation-reaction problem in classical electrodynamics still surprises and puzzles new generations of researchers. Here, we revise and explain some of the paradoxical issues that one faces when approaching the problem, mostly associated with regimes of uniform proper acceleration. The answers we provide can be found in the literature and are a synthesis of a large body of research. We only present them in a personal way that may help in their understanding. Besides, after the presentation of the standard answers, we motivate and present a twist to those ideas. The physics of emission of radiation by extended charges (charges with internal structure) might proceed in a surprising oscillating fashion. This hypothetical process could open up new research paths and a new take on the equivalence principle.
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38
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Chua AJK, Katz ML, Warburton N, Hughes SA. Rapid Generation of Fully Relativistic Extreme-Mass-Ratio-Inspiral Waveform Templates for LISA Data Analysis. PHYSICAL REVIEW LETTERS 2021; 126:051102. [PMID: 33605747 DOI: 10.1103/physrevlett.126.051102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2020] [Accepted: 11/20/2020] [Indexed: 06/12/2023]
Abstract
The future space mission LISA will observe a wealth of gravitational-wave sources at millihertz frequencies. Of these, the extreme-mass-ratio inspirals of compact objects into massive black holes are the only sources that combine the challenges of strong-field complexity with that of long-lived signals. Such signals are found and characterized by comparing them against a large number of accurate waveform templates during data analysis, but the rapid generation of templates is hindered by computing the ∼10^{3}-10^{5} harmonic modes in a fully relativistic waveform. We use order-reduction and deep-learning techniques to derive a global fit for the ≈4000 modes in the special case of an eccentric Schwarzschild orbit, and implement the fit in a complete waveform framework with hardware acceleration. Our high-fidelity waveforms can be generated in under 1 s, and achieve a mismatch of ≲5×10^{-4} against reference waveforms that take ≳10^{4} times longer. This marks the first time that analysis-length waveforms with full harmonic content can be produced on timescales useful for direct implementation in LISA analysis algorithms.
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Affiliation(s)
- Alvin J K Chua
- Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA
| | - Michael L Katz
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
- Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Evanston, Illinois 60208, USA
| | - Niels Warburton
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
| | - Scott A Hughes
- Department of Physics and MIT Kavli Institute, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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39
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Kälin G, Liu Z, Porto RA. Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach. PHYSICAL REVIEW LETTERS 2020; 125:261103. [PMID: 33449763 DOI: 10.1103/physrevlett.125.261103] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 12/01/2020] [Indexed: 06/12/2023]
Abstract
We derive the conservative dynamics of nonspinning binaries to third post-Minkowskian order, using the effective field theory (EFT) approach introduced in [G. Kälin and R. A. Porto, J. High Energy Phys. 11 (2020) 106JHEPFG1029-847910.1007/JHEP11(2020)106] together with the boundary-to-bound dictionary developed in [G. Kälin and R. A. Porto, J. High Energy Phys. 01 (2020) 072JHEPFG1029-847910.1007/JHEP01(2020)072; J. High Energy Phys. 02 (2020) 120.JHEPFG1029-847910.1007/JHEP02(2020)120]. The main ingredient is the scattering angle, which we compute to O(G^{3}) via Feynman diagrams. Adapting to the EFT framework powerful tools from the amplitudes program, we show how the associated (master) integrals are bootstrapped to all orders in velocities via differential equations. Remarkably, the boundary conditions can be reduced to the same integrals that appear in the EFT with post-Newtonian sources. For the sake of comparison, we reconstruct the Hamiltonian and the classical limit of the scattering amplitude. Our results are in perfect agreement with those in Bern et al. [Phys. Rev. Lett. 122, 201603 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.201603; J. High Energy Phys. 10 (2019) 206JHEPFG1029-847910.1007/JHEP10(2019)206].
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Affiliation(s)
- Gregor Kälin
- SLAC National Accelerator Laboratory, Stanford University, Stanford, California 94309, USA
| | - Zhengwen Liu
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
| | - Rafael A Porto
- Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany
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40
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Lousto CO, Healy J. Exploring the Small Mass Ratio Binary Black Hole Merger via Zeno's Dichotomy Approach. PHYSICAL REVIEW LETTERS 2020; 125:191102. [PMID: 33216595 DOI: 10.1103/physrevlett.125.191102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 07/30/2020] [Accepted: 09/11/2020] [Indexed: 06/11/2023]
Abstract
We perform a sequence of binary black hole simulations with increasingly small mass ratios, reaching to a 128:1 binary that displays 13 orbits before merger. Based on a detailed convergence study of the q=m_{1}/m_{2}=1/15 nonspinning case, we apply additional mesh refinement levels around the smaller hole horizon [30] to reach successively the q=1/32, q=1/64, and q=1/128 cases. Roughly a linear computational resources scaling with 1/q is observed on eight-nodes simulations. We compute the remnant properties of the merger: final mass, spin, and recoil velocity, finding precise consistency between horizon and radiation measures. We also compute the gravitational waveforms: their peak frequency, amplitude, and luminosity. We compare those values with predictions of the corresponding phenomenological formulas, reproducing the particle limit within 2%, and we then use the new results to improve their fitting coefficients.
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Affiliation(s)
- Carlos O Lousto
- Center for Computational Relativity and Gravitation, School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623, USA
| | - James Healy
- Center for Computational Relativity and Gravitation, School of Mathematical Sciences, Rochester Institute of Technology, 85 Lomb Memorial Drive, Rochester, New York 14623, USA
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41
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van de Meent M, Pfeiffer HP. Intermediate Mass-Ratio Black Hole Binaries: Applicability of Small Mass-Ratio Perturbation Theory. PHYSICAL REVIEW LETTERS 2020; 125:181101. [PMID: 33196223 DOI: 10.1103/physrevlett.125.181101] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 09/14/2020] [Indexed: 06/11/2023]
Abstract
The inspiral phasing of binary black holes at intermediate mass ratios (m_{2}/m_{1}∼10^{-3}) is important for gravitational wave observations, but not accessible to standard modeling techniques: The accuracy of the small mass-ratio (SMR) expansion is unknown at intermediate mass ratios, whereas numerical relativity simulations cannot reach this regime. This article assesses the accuracy of the SMR expansion by extracting the first three terms of the SMR expansion from numerical relativity data for nonspinning, quasicircular binaries. We recover the leading term predicted by SMR theory and obtain a robust prediction of the next-to-leading term. The influence of higher-order terms is bounded to be small, indicating that the SMR series truncated at next-to-leading order is quite accurate at intermediate mass ratios and even at nearly comparable mass binaries. We estimate the range of applicability for SMR and post-Newtonian series for nonspinning, quasicircular inspirals.
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Affiliation(s)
- Maarten van de Meent
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam, Germany
| | - Harald P Pfeiffer
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam, Germany
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Maselli A, Franchini N, Gualtieri L, Sotiriou TP. Detecting Scalar Fields with Extreme Mass Ratio Inspirals. PHYSICAL REVIEW LETTERS 2020; 125:141101. [PMID: 33064541 DOI: 10.1103/physrevlett.125.141101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 07/09/2020] [Accepted: 08/31/2020] [Indexed: 06/11/2023]
Abstract
We study extreme mass ratio inspirals (EMRIs), during which a small body spirals into a supermassive black hole, in gravity theories with additional scalar fields. We first argue that no-hair theorems and the properties of known theories that manage to circumvent them introduce a drastic simplification to the problem: the effects of the scalar on supermassive black holes, if any, are mostly negligible for EMRIs in vast classes of theories. We then exploit this simplification to model the inspiral perturbatively and we demonstrate that the scalar charge of the small body leaves a significant imprint on gravitational wave emission. Although much higher precision is needed for waveform modeling, our results strongly suggest that this imprint is observable with Laser Interferometer Space Antenna, rendering EMRIs promising probes of scalar fields.
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Affiliation(s)
- Andrea Maselli
- Dipartimento di Fisica, "Sapienza" Università di Roma & Sezione INFN Roma1, Piazzale Aldo Moro 5, 00185 Roma, Italy
| | - Nicola Franchini
- SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN Sezione di Trieste, via Valerio 2, 34127 Trieste, Italy
- IFPU-Institute for Fundamental Physics of the Universe, Via Beirut 2, 34014 Trieste, Italy
| | - Leonardo Gualtieri
- Dipartimento di Fisica, "Sapienza" Università di Roma & Sezione INFN Roma1, Piazzale Aldo Moro 5, 00185 Roma, Italy
| | - Thomas P Sotiriou
- School of Mathematical Sciences and School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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Antonelli A, Kavanagh C, Khalil M, Steinhoff J, Vines J. Gravitational Spin-Orbit Coupling through Third-Subleading Post-Newtonian Order: From First-Order Self-Force to Arbitrary Mass Ratios. PHYSICAL REVIEW LETTERS 2020; 125:011103. [PMID: 32678665 DOI: 10.1103/physrevlett.125.011103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2020] [Revised: 05/19/2020] [Accepted: 06/12/2020] [Indexed: 06/11/2023]
Abstract
Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes.
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Affiliation(s)
- Andrea Antonelli
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam 14476, Germany
| | - Chris Kavanagh
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam 14476, Germany
| | - Mohammed Khalil
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam 14476, Germany
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Jan Steinhoff
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam 14476, Germany
| | - Justin Vines
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam 14476, Germany
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Burke O, Gair J, Simón J. Transition from inspiral to plunge: A complete near-extremal trajectory and associated waveform. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.101.064026] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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45
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Pound A, Wardell B, Warburton N, Miller J. Second-Order Self-Force Calculation of Gravitational Binding Energy in Compact Binaries. PHYSICAL REVIEW LETTERS 2020; 124:021101. [PMID: 32004014 DOI: 10.1103/physrevlett.124.021101] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Revised: 10/10/2019] [Indexed: 06/10/2023]
Abstract
Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this Letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.
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Affiliation(s)
- Adam Pound
- School of Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
| | - Barry Wardell
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
| | - Niels Warburton
- School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland
| | - Jeremy Miller
- School of Mathematical Sciences and STAG Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
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Antonelli A, van de Meent M, Buonanno A, Steinhoff J, Vines J. Quasicircular inspirals and plunges from nonspinning effective-one-body Hamiltonians with gravitational self-force information. Int J Clin Exp Med 2020. [DOI: 10.1103/physrevd.101.024024] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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47
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Bini D, Geralico A. New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: Redshift invariant. Int J Clin Exp Med 2019. [DOI: 10.1103/physrevd.100.104002] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Bern Z, Cheung C, Roiban R, Shen CH, Solon MP, Zeng M. Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order. PHYSICAL REVIEW LETTERS 2019; 122:201603. [PMID: 31172785 DOI: 10.1103/physrevlett.122.201603] [Citation(s) in RCA: 43] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Indexed: 06/09/2023]
Abstract
We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. Adapting methods for integration and matching from effective field theory, we extract the conservative Hamiltonian for compact spinless binaries at third post-Minkowskian order. The resulting Hamiltonian is in complete agreement with corresponding terms in state-of-the-art expressions at fourth post-Newtonian order as well as the probe limit at all orders in velocity. We also derive the scattering angle at third post-Minkowskian order and find agreement with known results.
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Affiliation(s)
- Zvi Bern
- Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Clifford Cheung
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125
| | - Radu Roiban
- Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Chia-Hsien Shen
- Mani L. Bhaumik Institute for Theoretical Physics, University of California at Los Angeles, Los Angeles, California 90095, USA
| | - Mikhail P Solon
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125
| | - Mao Zeng
- Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
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