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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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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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Jakobsen GU, Mogull G, Plefka J, Sauer B, Xu Y. Conservative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order. PHYSICAL REVIEW LETTERS 2023; 131:151401. [PMID: 37897767 DOI: 10.1103/physrevlett.131.151401] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2023] [Accepted: 09/18/2023] [Indexed: 10/30/2023]
Abstract
Using the N=1 supersymmetric, spinning worldline quantum field theory formalism, we compute the conservative spin-orbit part of the momentum impulse Δp_{i}^{μ}, spin kick ΔS_{i}^{μ}, and scattering angle θ from the scattering of two spinning massive bodies (black holes or neutron stars) up to fourth post-Minkowskian (PM) order. These three-loop results extend the state of the art for generically spinning binaries from 3PM to 4PM. They are obtained by employing recursion relations for the integrand construction and advanced multiloop Feynman integral technology in the causal (in-in) worldline quantum field theory framework to directly produce classical observables. We focus on the conservative contribution (including tail effects) and outline the computations for the dissipative contributions as well. Our spin-orbit results agree with next-to-next-to-next-to-leading-order post-Newtonian and test-body data in the respective limits. We also reconfirm the conservative 4PM nonspinning results.
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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 Institute for Gravitational Physics (Albert Einstein Institute), 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 Institute for Gravitational Physics (Albert Einstein Institute), 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
| | - Yingxuan Xu
- Institut für Physik, Humboldt Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
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Heissenberg C. Angular Momentum Loss due to Tidal Effects in the Post-Minkowskian Expansion. PHYSICAL REVIEW LETTERS 2023; 131:011603. [PMID: 37478435 DOI: 10.1103/physrevlett.131.011603] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Revised: 04/25/2023] [Accepted: 06/06/2023] [Indexed: 07/23/2023]
Abstract
We calculate the tidal corrections to the loss of angular momentum in a two-body collision at leading post-Minkowskian order from an amplitude-based approach. The eikonal operator allows us to efficiently combine elastic and inelastic amplitudes, and captures both the contributions due to genuine gravitational-wave emissions and those due to the static gravitational field. We calculate the former by harnessing powerful collider-physics techniques such as reverse unitarity, thereby reducing them to cut two-loop integrals, and cross check the result by performing an independent calculation in the post-Newtonian limit. For the latter, we can employ the results of P. Di Vecchia et al. [Angular momentum of zero-frequency gravitons, J. High Energy Phys. 08 (2022) 172.JHEPFG1029-847910.1007/JHEP08(2022)172], where static-field effects were calculated for generic gravitational scattering events using the leading soft graviton theorem.
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Affiliation(s)
- Carlo Heissenberg
- Department of Physics and Astronomy, Uppsala University, Box 516, SE-75237 Uppsala, Sweden and NORDITA, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-11419, Stockholm, Sweden
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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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Cordero FF, Kraus M, Lin G, Ruf MS, Zeng M. Conservative Binary Dynamics with a Spinning Black Hole at O(G^{3}) from Scattering Amplitudes. PHYSICAL REVIEW LETTERS 2023; 130:021601. [PMID: 36706419 DOI: 10.1103/physrevlett.130.021601] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2022] [Revised: 09/15/2022] [Accepted: 11/29/2022] [Indexed: 06/18/2023]
Abstract
We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through O(G^{3}) to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numerical unitarity, integration-by-parts identities, and the method of regions. The conservative potential in terms of rest-frame spin vectors is extracted by matching to a nonrelativistic effective field theory. We also apply the Kosower-Maybee-O'Connell (KMOC) formalism to calculate the impulse in the covariant spin formalism directly from the amplitude. We work systematically in conventional dimensional regularization and explicitly evaluate all divergent integrals that appear in full- and effective-theory amplitudes, as well as in the phase-space integrals that arise in the KMOC formalism.
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Affiliation(s)
| | - Manfred Kraus
- Physics Department, Florida State University, Tallahassee, Florida 32306-4350, USA
| | - Guanda Lin
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- Higgs Centre for Theoretical Physics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Michael S Ruf
- 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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Aoude R, Haddad K, Helset A. Classical Gravitational Spinning-Spinless Scattering at O(G^{2}S^{∞}). PHYSICAL REVIEW LETTERS 2022; 129:141102. [PMID: 36240407 DOI: 10.1103/physrevlett.129.141102] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Revised: 07/22/2022] [Accepted: 09/15/2022] [Indexed: 06/16/2023]
Abstract
Making use of the recently derived, all-spin, opposite-helicity Compton amplitude, we calculate the classical gravitational scattering amplitude for one spinning and one spinless object at O(G^{2}) and all orders in spin. By construction, this amplitude exhibits the spin structure that has been conjectured to describe Kerr black holes. This spin structure alone is not enough to fix all deformations of the Compton amplitude by contact terms, but when combined with considerations of the ultrarelativistic limit we can uniquely assign values to the parameters remaining in the even-in-spin sector. Once these parameters are determined, much of the spin dependence of the amplitude resums into hypergeometric functions. Finally, we derive the eikonal phase for aligned-angular-momentum scattering.
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Affiliation(s)
- Rafael Aoude
- Centre for Cosmology, Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
| | - Kays Haddad
- Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden
- Nordita, Stockholm University and KTH Royal Institute of Technology, Hannes Alfvéns väg 12, 10691 Stockholm, Sweden
| | - Andreas Helset
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
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