Self-gravitating ring of matter in orbit around a black hole: The innermost stable circular orbit

Abstract

We study analytically a black-hole-ring system which is composed of a stationary axisymmetric ring of particles in orbit around a perturbed Kerr black hole of mass $M$. In particular, we calculate the shift in the orbital frequency of the innermost stable circular orbit (ISCO) due to the finite mass $m$ of the orbiting ring. It is shown that for thin rings of half-thickness $r\ll M$, the dominant finite-mass correction to the characteristic ISCO frequency stems from the self-gravitational potential energy of the ring (a term in the energy budget of the system which is quadratic in the mass $m$ of the ring). This dominant correction to the ISCO frequency is of order $O(\mu \ln (M/r))$, where $\mu \equiv m/M$ is the dimensionless mass of the ring. We show that the ISCO frequency increases (as compared to the ISCO frequency of an orbiting test-ring) due to the finite-mass effects of the self-gravitating ring.

arXiv comment11 pages

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Cited by in corpus (10)

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• Innermost stable circular orbits of charged spinning test particles
• Motion deviation of test body induced by spin and cosmological constant in extreme mass ratio inspiral binary system
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• The evolutions of the innermost stable circular orbits in dynamical spacetimes
• Perturbation of a Schwarzschild black hole due to a rotating thin disc
• Dragging of inertial frames in the composed black-hole-ring system
• Collision of particles near charged MSW black hole in 2 + 1 dimensions
• Marginally bound circular orbits in the composed black-hole-ring system