Exploring New Physics Frontiers Through Numerical Relativity

Effective Field Theory for Extreme Mass Ratio Binaries

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.

Quantum Precision Limits of Displacement Noise-Free Interferometers

Current laser-interferometric gravitational wave detectors suffer from a fundamental limit to their precision due to the displacement noise of optical elements contributed by various sources. Several schemes for displacement noise-free interferometers (DFI) have been proposed to mitigate their effects. The idea behind these schemes is similar to decoherence-free subspaces in quantum sensing; i.e., certain modes contain information about the gravitational waves but are insensitive to the mirror motion (displacement noise). We derive quantum precision limits for general DFI schemes, including optimal measurement basis and optimal squeezing schemes. We introduce a triangular cavity DFI scheme and apply our general bounds to it. Precision analysis of this scheme with different noise models shows that the DFI property leads to interesting sensitivity profiles and improved precision due to noise mitigation and larger gain from squeezing.

Ultimate Black Hole Recoil: What is the Maximum High-Energy Collision Kick?

We performed a series of 1381 full numerical simulations of high energy collision of black holes to search for the maximum recoil velocity after their merger. We consider equal mass binaries with opposite spins pointing along their orbital plane and perform a search of spin orientations, impact parameters, and initial linear momenta to find the maximum recoil for a given spin magnitude s. This spin sequence for s=0.4, 0.7, 0.8, 0.85, 0.9 is then extrapolated to the extreme case, s=1, to obtain an estimated maximum recoil velocity of 28,562±342  km/s, thus approximately bounded by 10% of the speed of light.

Gravitational waves at the first post-Newtonian order with the Weyssenhoff fluid in Einstein-Cartan theory

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.

An exact integral-to-sum relation for products of Bessel functions

A useful identity relating the infinite sum of two Bessel functions to their infinite integral was discovered in Dominici et al. (Dominici et al. 2012 Proc. R. Soc. A 468 , 2667–2681). Here, we extend this result to products of N Bessel functions, and show it can be straightforwardly proven using the Abel-Plana theorem, or the Poisson summation formula. For N  = 2, the proof is much simpler than that of Dominici et al. and significantly enlarges the range of validity.

Vacuum Energy Decay from a q-Bubble

We consider a finite-size spherical bubble with a nonequilibrium value of the q-field, where the bubble is immersed in an infinite vacuum with the constant equilibrium value q 0 for the q-field (this q 0 has already cancelled an initial cosmological constant). Numerical results are presented for the time evolution of such a q-bubble with gravity turned off and with gravity turned on. For small enough bubbles and a q-field energy scale sufficiently below the gravitational energy scale E Planck , the vacuum energy of the q-bubble is found to disperse completely. For large enough bubbles and a finite value of E Planck , the vacuum energy of the q-bubble disperses only partially and there occurs gravitational collapse near the bubble center.

Gravitational Waves in Massive Gravity Theories: Waveforms, Fluxes, and Constraints from Extreme-Mass-Ratio Mergers

Is the graviton massless? This problem was addressed in the literature at a phenomenological level, using modified dispersion relations for gravitational waves, in linearized calculations around flat space. Here, we perform a detailed analysis of the gravitational waveform produced when a small particle plunges or inspirals into a large nonspinning black hole. Our results should presumably also describe the gravitational collapse to black holes and explosive events such as supernovae. In the context of a theory with massive gravitons and screening, merging objects up to 1 Gpc away or collapsing stars in the nearby galaxy may be used to constrain the mass of the graviton to be smaller than ∼10^{-23}  eV, with low-frequency detectors. Our results suggest that the absence of dipolar gravitational waves from black hole binaries may be used to rule out entirely such theories.

Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics

We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into general relativity (GR) coupled to another nonlinear theory of electrodynamics. This allows to generate solutions of the former from those of the latter using purely algebraic transformations. This correspondence is explicitly illustrated with the Eddington-inspired Born-Infeld theory of gravity, for which we consider a family of nonlinear electrodynamics and show that, under the map, preserve their algebraic structure. For the particular case of Maxwell electrodynamics coupled to Born-Infeld gravity we find, via this correspondence, a Born-Infeld-type nonlinear electrodynamics on the GR side. Solving the spherically symmetric electrovacuum case for the latter, we show how the map provides directly the right solutions for the former. This procedure opens a new door to explore astrophysical and cosmological scenarios in nonlinear gravity theories by exploiting the full power of the analytical and numerical methods developed within the framework of GR.

Fundamentals of numerical relativity for gravitational wave sources

Einstein's theory of general relativity affords an enormously successful description of gravity. The theory encodes the gravitational interaction in the metric, a tensor field on spacetime that satisfies partial differential equations known as the Einstein equations. This review introduces some of the fundamental concepts of numerical relativity-solving the Einstein equations on the computer-in simple terms. As a primary example, we consider the solution of the general relativistic two-body problem, which features prominently in the new field of gravitational wave astronomy.

New theories of relativistic hydrodynamics in the LHC era

The success of relativistic hydrodynamics as an essential part of the phenomenological description of heavy-ion collisions at RHIC and the LHC has motivated a significant body of theoretical work concerning its fundamental aspects. Our review presents these developments from the perspective of the underlying microscopic physics, using the language of quantum field theory, relativistic kinetic theory, and holography. We discuss the gradient expansion, the phenomenon of hydrodynamization, as well as several models of hydrodynamic evolution equations, highlighting the interplay between collective long-lived and transient modes in relativistic matter. Our aim to provide a unified presentation of this vast subject-which is naturally expressed in diverse mathematical languages-has also led us to include several new results on the large-order behaviour of the hydrodynamic gradient expansion.

Effects of Nonlinear Inhomogeneity on the Cosmic Expansion with Numerical Relativity

We construct a three-dimensional, fully relativistic numerical model of a universe filled with an inhomogeneous pressureless fluid, starting from initial data that represent a perturbation of the Einstein-de Sitter model. We then measure the departure of the average expansion rate with respect to this homogeneous and isotropic reference model, comparing local quantities to the predictions of linear perturbation theory. We find that collapsing perturbations reach the turnaround point much earlier than expected from the reference spherical top-hat collapse model and that the local deviation of the expansion rate from the homogeneous one can be as high as 28% at an underdensity, for an initial density contrast of 10^{-2}. We then study, for the first time, the exact behavior of the backreaction term Q_{D}. We find that, for small values of the initial perturbations, this term exhibits a 1/a scaling, and that it is negative with a linearly growing absolute value for larger perturbation amplitudes, thereby contributing to an overall deceleration of the expansion. Its magnitude, on the other hand, remains very small even for relatively large perturbations.

New Features of Gravitational Collapse in Anti-de Sitter Spacetimes

Gravitational collapse of a massless scalar field in spherically symmetric anti-de Sitter (AdS) spacetimes presents a new phenomenology with a series of critical points whose dynamics is discretely self-similar as in the asymptotically flat case. Each critical point is the limit of a branch of scalar field configurations that have bounced off the AdS boundary a fixed number of times before forming an apparent horizon. We present results from a numerical study that focus on the interfaces between branches. We find that there is a mass gap between branches and that subcritical configurations near the critical point form black holes with an apparent horizon mass that follows a power law of the form M(AH)-M(g)∝(p(c)-p)^(ξ), where M(g) is the mass gap and the exponent ξ≃0.7 appears to be universal.