# What is a singular black hole beyond General Relativity?

## TL;DR

This paper investigates singular black hole spacetimes in quadratic $f(R)$ gravity coupled with an anisotropic fluid, revealing diverse configurations and challenging the notion of singularities in quantum gravity.

## Contribution

It introduces minimal extensions of GR using metric-affine $f(R)$ gravity with anisotropic fluids, exploring their impact on black hole singularities and horizon structures.

## Key findings

- Discovery of configurations with and without wormholes
- Identification of solutions with de Sitter interiors
- Presence of up to four horizons in certain models

## Abstract

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.