Time-domain metric reconstruction for hyperbolic scattering

Abstract

Self-force methods can be applied in calculations of the scatter angle in two-body hyperbolic encounters, working order by order in the mass ratio (assumed small) but with no recourse to a weak-field approximation. This, in turn, can inform ongoing efforts to construct an accurate model of the general-relativistic binary dynamics via an effective-one-body description and other semi-analytical approaches. Existing self-force methods are to a large extent specialised to bound, inspiral orbits. Here we develop a technique for (numerical) self-force calculations that can efficiently tackle scatter orbits. The method is based on a time-domain reconstruction of the metric perturbation from a scalar-like Hertz potential that satisfies the Teukolsky equation, an idea pursued so far only for bound orbits. The crucial ingredient in this formulation are certain jump conditions that (each multipole mode of) the Hertz potential must satisfy along the orbit, in a 1+1-dimensional multipole reduction of the problem. We obtain a closed-form expression for these jumps, for an arbitrary geodesic orbit in Schwarzschild spacetime, and present a full numerical implementation for a scatter orbit. In this paper we focus on method development, and go only as far as calculating the Hertz potential; a calculation of the self-force and its physical effects on the scatter orbit will be the subject of forthcoming work.

arXiv comment28 pages, 11 figures; v3 corrected typo in Eq. (103); v5 corrected typo in Eq. (A12)

References in corpus (47)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Gravitational self force in extreme mass-ratio inspirals
• High-energy gravitational scattering and the general relativistic two-body problem
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• From Boundary Data to Bound States
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Classical and quantum scattering in post-Minkowskian gravity
• Superradiant instabilities of rotating black holes in the time domain
• Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
• Radiative contribution to classical gravitational scattering at the third order in $G$
• The Tune of Love and the Nature(ness) of Spacetime
• Gravitational self-force on generic bound geodesics in Kerr spacetime
• Gravitational waveforms from a point particle orbiting a Schwarzschild black hole
• Gravitational self force and gauge transformations
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Gravitational Self-force in a Radiation Gauge
• Gravitational self-force from radiation-gauge metric perturbations
• Scalar self-force on eccentric geodesics in Schwarzschild spacetime: a time-domain computation
• Reconstruction of Black Hole Metric Perturbations from Weyl Curvature
• Completion of metric reconstruction for a particle orbiting a Kerr black hole
• Late time dynamics of scalar perturbations outside black holes: II. Schwarzschild geometry
• Frequency-domain calculation of the self force: the high-frequency problem and its resolution
• Numerical solution of the 2+1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late-time decays
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• Teukolsky formalism for nonlinear Kerr perturbations
• Numerical investigation of the late-time Kerr tails
• On finding fields and self-force in a gauge appropriate to separable wave equations
• Late time decay of scalar, electromagnetic, and gravitational perturbations outside rotating black holes
• Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
• Perturbative evolution of particle orbits around Kerr black holes: time domain calculation
• Intermediate behavior of Kerr tails
• A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit
• The mass and angular momentum of reconstructed metric perturbations
• Teukolsky evolution of particle orbits around Kerr black holes in the time domain: elliptic and inclined orbits
• Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits
• Cauchy-horizon singularity inside perturbed Kerr black holes
• Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
• Scattering of point particles by black holes: gravitational radiation
• Unbound motion on a Schwarzschild background: Practical approaches to frequency domain computations
• Excitation of Kerr quasinormal modes in extreme--mass-ratio inspirals
• Linearized Stability of Extreme Black Holes
• Time-domain metric reconstruction for self-force applications
• Characteristic formulation of the Regge-Wheeler and Zerilli Green functions
• The Marolf-Ori singularity inside fast spinning black holes

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• The Science of the Einstein Telescope
• Effective Field Theory for Extreme Mass Ratios
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• New metric reconstruction scheme for gravitational self-force calculations
• Self-force correction to the deflection angle in black-hole scattering: a scalar charge toy model
• Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory
• Frequency-domain approach to self-force in hyperbolic scattering
• Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation
• Conservative Scattering of Reissner-Nordström Black Holes at Third Post-Minkowskian Order
• Gravitational radiation from hyperbolic orbits: comparison between self-force, post-Minkowskian, post-Newtonian, and numerical relativity results
• Frequency-domain self-force calculations using Gegenbauer reconstruction