Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What is a singular black hole beyond General Relativity?   Exploring the characterization of singular black hole spacetimes, we study
the relation between energy density, curvature invariants, and geodesic
completeness using a quadratic $f(R)$ gravity theory coupled to an anisotropic
fluid. Working in a metric-affine approach, our models and solutions represent
minimal extensions of General Relativity (GR) in the sense that they rapidly
recover the usual Reissner-Nordstr\"{o}m solution from near the inner horizon
outwards. The anisotropic fluid helps modify only the innermost geometry.
Depending on the values and signs of two parameters on the gravitational and
matter sectors, a breakdown of the correlations between the
finiteness/divergence of the energy density, the behavior of curvature
invariants, and the (in)completeness of geodesics is obtained. We find a
variety of configurations with and without wormholes, a case with a de Sitter
interior, solutions that mimic non-linear models of electrodynamics coupled to
GR, and configurations with up to four horizons. Our results raise questions
regarding what infinities, if any, a quantum version of these theories should
regularize.

35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
18
The categories of this paper are: econ