Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Shadow of a Schwarzschild black hole surrounded by a Bach-Weyl ring
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics