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Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
By Soichiro Isoyama, Leor Barack, Sam R. Dolan, Alexandre Le Tiec, Hiroyuki Nakano, Abhay G. Shah, Takahiro Tanaka, Niels Warburton
Published in Physical Review Letters 113, 161101 (Wednesday, October 15, 2014)

Abstract

For a self-gravitating particle of mass \mu in orbit around a Kerr black hole of mass M >> \mu, we compute the O(\mu/M) shift in the frequency of the innermost stable circular equatorial orbit (ISCEO) due to the conservative piece of the gravitational self-force acting on the particle. Our treatment is based on a Hamiltonian formulation of the dynamics in terms of geodesic motion in a certain locally-defined effective smooth spacetime. We recover the same result using the so-called first law of binary black-hole mechanics. We give numerical results for the ISCEO frequency shift as a function of the black hole's spin amplitude, and compare with predictions based on the post-Newtonian approximation and the effective one-body model. Our results provide an accurate strong-field benchmark for spin effects in the general relativistic two-body problem.