Singularity resolution by holonomy corrections: Spherical charged black holes in cosmological backgrounds

TL;DR

This paper investigates how loop quantum gravity inspired corrections can resolve singularities in spherical charged black holes within a cosmological background, resulting in a globally regular spacetime under certain parameter conditions.

Contribution

The study introduces a Hamiltonian-based effective theory with holonomy corrections that ensures covariance and constructs a nonsingular black hole solution in a cosmological setting.

Findings

Singularity-free solutions exist for nonnegative mass and cosmological constant.

The charge must be relatively small and bounded for the spacetime to be nonsingular.

The model provides a globally regular description of astrophysical black holes in de Sitter backgrounds.

Abstract

We study spherical charged black holes in the presence of a cosmological constant with corrections motivated by the theory of loop quantum gravity. The effective theory is constructed at the Hamiltonian level by introducing certain correction terms under the condition that the modified constraints form a closed algebra. The corresponding metric tensor is then carefully constructed ensuring that the covariance of the theory is respected, that is, in such a way that different gauge choices on phase space simply correspond to different charts of the same spacetime solution. The resulting geometry is characterized by four parameters: the three usual ones that appear in the general relativistic limit (describing the mass, the charge, and the cosmological constant), as well as a polymerization parameter, which encodes the quantum-gravity corrections. Contrary to general relativity, where this family of solutions is generically singular, in this effective model the presence of the singularity depends on the values of the parameters. The specific ranges of values that define the family of singularity-free spacetimes are explicitly found, and their global structure is analyzed. In particular, the mass and the cosmological constant need to be nonnegative to provide a nonsingular geometry, while there can only be a bounded, relatively small, amount of charge. These conditions are suited for any known spherical astrophysical black hole in the de Sitter cosmological background, and thus this model provides a globally regular description for them.