期刊
PHYSICAL REVIEW D
卷 94, 期 10, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.94.104066
关键词
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资金
- CONACyT
- European Research Council under the European Union's Seventh Framework Programme FP7/ERC [304978]
- STFC [PP/E001025/1]
- STFC [PP/C505791/1, PP/E001025/1, ST/M000931/1] Funding Source: UKRI
- Science and Technology Facilities Council [PP/E001025/1, ST/M000931/1] Funding Source: researchfish
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 et al. for circular orbits and extend them to noncircular orbits.
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