Quantum field theory-inspired cure for black hole singularities

TL;DR

This paper introduces a systematic exponential cutoff regularization scheme for static black holes in general relativity, effectively smoothing singularities while preserving asymptotic properties and offering a unified framework for singularity-free black hole models.

Contribution

The paper proposes a novel exponential cutoff regularization method for black hole solutions, providing an alternative to existing regularization mechanisms and ensuring geodesic completeness without altering asymptotic structure.

Findings

Regularized Schwarzschild black hole avoiding singularities

Presented a new regularized Kiselev solution

Maintained physical consistency and thermodynamic properties

Abstract

In recent years, there has been a growing interest in the study of regular black holes, driven by the search for singularity-free geometries. This research has revealed intriguing similarities between the regularization mechanisms used in black hole models and those employed in quantum field theory, such as the introduction of exponential suppression or energy cutoffs. We propose a systematic exponential cutoff regularization scheme for static, spherically symmetric black hole solutions in general relativity. The method explored in this paper serves as an alternative to the black-bounce singularity suppression mechanism proposed by Simpson and Visser, which involves a coordinate remapping $r \rightarrow\sqrt{r^2+a^2}$, as well as to the mechanism proposed by Bronnikov, which employs a Bardeen-type remapping in the metric. The method presented here introduces exponential factors in the mass function, smoothing curvature divergences and ensuring geodesic completeness under specific conditions. This approach allows the regularization of known singular spacetimes without altering their asymptotic structure. We analyze curvature invariants, horizon formation, and thermodynamic properties, showing that the regularized geometries avoid singularities while maintaining physical consistency. As examples of application, we regularize the Schwarzschild black hole and present a novel regularized Kiselev solution. The method provides a unified framework to systematically generate singularity-free black holes within classical general relativity