Quantum field theory-inspired cure for black hole singularities

TL;DR

This work addresses curvature singularities in black holes by introducing a quantum-field-theory–inspired exponential cutoff regularization for static, spherically symmetric spacetimes. The central idea is to modify the mass function via $M(r)=m(r)\exp(-a^{n+1}/r^{n+1})$, which suppresses divergences while preserving asymptotic behavior, and to analyze resulting curvature invariants, geodesic completeness, and horizons. The authors develop the formalism, derive an anisotropic-fluid source, and examine a Dymnikova-type alternative, illustrating the method with Schwarzschild and a novel regular Kiselev solution; they show that geodesic completeness depends on the regulator exponent $n$ and that horizon structure can be expressed with the Lambert $W$ function. The approach offers a flexible framework to generate singularity-free black holes within classical GR and suggests extensions to rotating spacetimes and potential observational signatures.

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

Figures (3)

• Figure 1: The plot shows a general metric solution $B(r)$ with $m(r)$ exhibiting a subexponential growth as a function of the radial coordinate $r$ for different values of the parameter $n$, with fixed parameters $a = 1/4$ and $M = 1$.
• Figure 2: The plot shows the effective potential $V(r)$ as a function of the radial coordinate $r$ for different values of the parameter $n$, with fixed parameters $a = 1/4$ and $M = 1$. As $n$ increases from 0 to 3, the shape of the potential changes significantly. For negative values of $r$, the potential becomes steeper and more repulsive with increasing $n$. Near $r = 0$, a pronounced potential well appears, whose depth and profile vary depending on $n$, indicating the presence of a strong interaction in this region.
• Figure 3: The plot shows a metric solution $B(r)$ with $m(r)$ being the Kiselv solution as a function of the radial coordinate $r$ for different values of the parameter $w$, with fixed parameters $a = 1/4$, $M = 1$ and $n=1$.