Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singularity theorems in Schwarzschild spacetimes   We present a review of the two prominent singularity theorems due to Penrose
and Hawking, as well as their physical interpretation. Their usage is discussed
in detail for the Schwarzschild spacetime with positive and negative mass.
First, we present a detailed mathematical proof to formally guarantee the
existence of a singularity of geodesic incompleteness for the case of positive
mass. Second, we discuss the applicability of the mathematical tools used by
the theorems in the negative mass case. The physical implications of the
validity or inconsistency of the hypotheses of such theorems on the latter
case, are also exhibited. As far as this analysis is concerned, some clues are
produced regarding future research that could result in general properties for
naked singularities.

11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org