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.

11 pages

References in corpus (4)

• Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole
• Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge
• Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods
• Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: a new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force

Cited by in corpus (6)

• Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole
• Innermost stable circular orbits of charged spinning test particles
• Spinning Particle Dynamics and ISCO in Covariant Loop Quantum Gravity
• The evolutions of the innermost stable circular orbits in dynamical spacetimes
• Collision of particles near charged MSW black hole in 2 + 1 dimensions
• Marginally bound circular orbits in the composed black-hole-ring system