Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole

Abstract

For a self-gravitating particle of mass μin orbit around a Kerr black hole of mass M >> μ, we compute the O(μ/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.

5 pages, 1 table, 1 figure, matches version published in PRL. Raw data of H_int/mu are available at http://link.aps.org/supplemental/10.1103/PhysRevLett.113.161101

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• Importance of transient resonances in extreme-mass-ratio inspirals
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• Stable circular orbits of spinning test particles around accelerating Kerr black hole