Time-domain metric reconstruction for self-force applications

Abstract

We present a new method for calculation of the gravitational self-force (GSF) in Kerr geometry, based on a time-domain reconstruction of the metric perturbation from curvature scalars. In this approach, the GSF is computed directly from a certain scalar-like self-potential that satisfies the time-domain Teukolsky equation on the Kerr background. The approach is computationally much cheaper than existing time-domain methods, which rely on a direct integration of the linearized Einstein's equations and are impaired by mode instabilities. At the same time, it retains the utility and flexibility of a time-domain treatment, allowing calculations for any type of orbit (including highly eccentric or unbound ones) and the possibility of self-consistently evolving the orbit under the effect of the GSF. Here we formulate our method, and present a first numerical application, for circular geodesic orbits in Schwarzschild geometry. We discuss further applications.

arXiv comment21 pages, 7 figures; v3 corrects typo in Eq. (58)

References in corpus (40)

• The motion of point particles in curved spacetime
• Gravitational self force in extreme mass-ratio inspirals
• Mode sum regularization approach for the self-force in black hole spacetime
• Superradiant instabilities of rotating black holes in the time domain
• A Rigorous Derivation of Gravitational Self-force
• Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
• Second-order gravitational self-force
• Gravitational self force on a particle in circular orbit around a Schwarzschild black hole
• Gravitational self force and gauge transformations
• Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation
• Second Order Gravitational Self-Force
• Gravitational Self-force in a Radiation Gauge
• Reconstruction of inhomogeneous metric perturbations and electromagnetic four-potential in Kerr spacetime
• Regularization of fields for self-force problems in curved spacetime: foundations and a time-domain application
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms
• Gravitational self-force on a particle orbiting a Kerr black hole
• Gravitational self-force from radiation-gauge metric perturbations
• A practical, covariant puncture for second-order self-force calculations
• Reconstruction of Black Hole Metric Perturbations from Weyl Curvature
• Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
• Self-force corrections to the periapsis advance around a spinning black hole
• Completion of metric reconstruction for a particle orbiting a Kerr black hole
• m-Mode Regularization Scheme for the Self Force in Kerr Spacetime
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• 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
• Frequency-domain algorithm for the Lorenz-gauge gravitational self-force
• Second-order perturbation theory: problems on large scales
• Inspiral into Gargantua
• Perturbative evolution of particle orbits around Kerr black holes: time domain calculation
• Second-order perturbation theory: the problem of infinite mode coupling
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• A conservative effect of the second-order gravitational self-force on quasicircular orbits in Schwarzschild spacetime
• A time-domain fourth-order-convergent numerical algorithm to integrate black hole perturbations in the extreme-mass-ratio limit
• Late-time decay of gravitational and electromagnetic perturbations along the event horizon
• Mode coupling mechanism for late-time Kerr tails
• Self-force: Computational Strategies
• Cauchy-horizon singularity inside perturbed Kerr black holes
• Self-force from reconstructed metric perturbations: numerical implementation in Schwarzschild spacetime

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• Self-force effects on the marginally bound zoom-whirl orbit in Schwarzschild spacetime
• Time-domain metric reconstruction for hyperbolic scattering
• New self-force method via elliptic partial differential equations for Kerr inspiral models
• Gauge-fixing for the completion problem of reconstructed metric perturbations of a Kerr spacetime
• Scalar Self-force for High Spin Black Holes
• Toward exponentially-convergent simulations of extreme-mass-ratio inspirals: A time-domain solver for the scalar Teukolsky equation with singular source terms
• Discontinuous collocation methods and gravitational self-force applications
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