Completion of metric reconstruction for a particle orbiting a Kerr black hole

Abstract

Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in either of the two Weyl scalars ${\psi }_0$ or ${\psi }_4$, using a procedure described by Chrzanowski and others in the 1970s. More recent work, motivated within the context of self-force physics, extends the procedure to metric perturbations sourced by a particle in a bound geodesic orbit. However, the existing procedure leaves undetermined a certain stationary, axially-symmetric piece of the metric perturbation. In the vacuum region away from the particle, this "completion" piece corresponds simply to mass and angular-momentum perturbations of the Kerr background, with amplitudes that are, however, a priori unknown. Here we present and implement a rigorous method for finding the completion piece. The key idea is to impose continuity, off the particle, of certain gauge-invariant fields constructed from the full (completed) perturbation, in order to determine the unknown amplitude parameters of the completion piece. We implement this method in full for bound (eccentric) geodesic orbits in the equatorial plane of the Kerr black hole. Our results provide a rigorous underpinning of recent results by Friedman {\it et al.}\ for circular orbits, and extend them to non-circular orbits.

arXiv comment27 pages, Minor typos corrected

References in corpus (19)

• The motion of point particles in curved spacetime
• Gravitational self force in extreme mass-ratio inspirals
• Gravitational self force and gauge transformations
• Gravitational Self-force in a Radiation Gauge
• Reconstruction of inhomogeneous metric perturbations and electromagnetic four-potential in Kerr spacetime
• EMRI corrections to the angular velocity and redshift factor of a mass in circular orbit about a Kerr black hole
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge
• Gravitational self-force from radiation-gauge metric perturbations
• Reconstruction of Black Hole Metric Perturbations from Weyl Curvature
• Gravitational self-force on eccentric equatorial orbits around a Kerr black hole
• Frequency-domain calculation of the self force: the high-frequency problem and its resolution
• 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
• Linear-in-mass-ratio contribution to spin precession and tidal invariants in Schwarzschild spacetime at very high post-Newtonian order
• Late-time decay of gravitational and electromagnetic perturbations along the event horizon
• On the Existence of Radiation Gauges in Petrov type II spacetimes
• Self-force from reconstructed metric perturbations: numerical implementation in Schwarzschild spacetime
• Gravitational field of a Schwarzschild black hole and a rotating mass ring

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