期刊
PHYSICAL REVIEW D
卷 92, 期 6, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.92.064025
关键词
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资金
- NWO Rubicon Grant [680-50-1203]
- European Research Council under European Union's Seventh Framework Programme/ERC Grant [304978]
We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar. 4 using semianalytical methods. The metric perturbation is then reconstructed from. 4 in an (outgoing) radiation gauge, adding the appropriate nonradiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift U as a function of the orbital frequencies Omega(r) and Omega(phi) to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of U. In Kerr, we provide completely novel values of U for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.
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