Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The gravitational two-body problem in the vicinity of the light ring:
  Insights from the black-hole-ring toy model   The physical properties of an axisymmetric black-hole-ring system are studied
analytically within the framework of general relativity to second order in the
dimensionless mass ratio $\mu\equiv m/M$. In particular, we analyze the
asymptotic behaviors of the binding-energy and the total angular-momentum of
the two-body system in the vicinity of the light ring at $R=3M$, where the
circular orbit becomes null. We find that both quantities diverge {\it
quadratically} in $\mu(1-3M/R)^{-1}$ at the light ring. The reported divergent
behavior of the physical quantities stems from the second order spin-orbit
interaction between the black hole and the orbiting object (the dragging of
inertial frames by the orbiting ring). It is shown that this composed
black-hole-ring toy model captures some of the essential features of the
conservative dynamics of the (astrophysically more interesting)
black-hole-particle system. In particular, we show that both systems share the
{\it same} quadratic divergent behavior of the physical quantities near the
light ring. Moreover, we prove that both systems are characterized by the {\it
same} ratio ${{E^{(2)}(R\to 3M)}\over{J^{(2)}(R\to
3M)}}={{1}\over{3\sqrt{3}}}$, where $E^{(2)}$ and $J^{(2)}$ are the divergent
second order (self-interaction) expansion coefficients of the binding-energies
and the angular-momenta of the systems, respectively.

14
The categories of this paper are: math-ph
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex