Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-gravitating ring of matter in orbit around a black hole: The
  innermost stable circular orbit   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.

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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ