Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole

Van De Meent, Maarten and Shah, Abhay G. (2015) Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole. Physical Review D, 92 (6), 1-26. (doi:10.1103/PhysRevD.92.064025).

Record type: Article

Abstract

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 ?r and ?? 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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