Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbits around a Kerr black hole and its shadow   Since the full General Theory of Relativity has been unveiled to the
scientific community in 1915, many solutions to the vacuum Einstein field
equations have been found and studied. This paper aims at documenting
exhaustively the derivation of the shape of the patch of the sky that is left
completely black by a spinning black hole described by the Kerr solutions in
Boyer-Lindquist coordinates. This dark zone in the observer's sky is called the
black hole shadow. Conserved quantities which allow for the analysis of
particle orbits are first introduced, with the help of which the trajectories
of photons are uniquely described by two impact parameters (Specific angular
momentum in the azimuthal direction L and dimensionless Carter's constant Q).
We then derive the conditions on those parameters required for a photon to be
captured by the black hole. These conditions are then translated into an
equation for the black hole shadow. We conclude the paper by drawing out the
black hole shadows for an equatorial observer for two separate cases.

12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat