https://doi.org/10.1140/epjc/s10052-014-2840-4
Regular Article - Theoretical Physics
Self-gravitating ring of matter in orbit around a black hole: the innermost stable circular orbit
1
The Ruppin Academic Center, Emeq Hefer, 40250, Israel
2
The Hadassah Institute, Jerusalem, 91010, Israel
* e-mail: shaharhod@gmail.com
Received:
2
February
2014
Accepted:
27
March
2014
Published online:
11
April
2014
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 
. In particular, we calculate the shift in the orbital frequency of the innermost stable circular orbit (ISCO) due to the finite mass 
of the orbiting ring. It is shown that for thin rings of half-thickness 
, 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 of the ring). This dominant correction to the ISCO frequency is of order 
, where 
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.
© SIF and Springer-Verlag Berlin Heidelberg, 2014
