Nonsingular spherically symmetric black-hole model with holonomy corrections

TL;DR

This paper introduces a covariant, loop quantum gravity-inspired black hole model that replaces the singularity with a minimal spacelike hypersurface, ensuring anomaly-free modifications and a well-defined global spacetime structure.

Contribution

It presents a novel covariant black hole solution with holonomy corrections that remains free of anomalies and generalizes classical solutions with a nonsingular core.

Findings

The model is asymptotically flat with a well-defined ADM mass.

It features a nonsingular black-hole/white-hole region with a minimal hypersurface.

The solution's global causal structure and maximal extension are explicitly constructed.

Abstract

We present a covariant model of a spherically symmetric black hole with corrections motivated by loop quantum gravity. The effective modifications, parametrized by a positive constant $\lambda$, are implemented through a canonical transformation and a linear combination of the constraints of general relativity, in such a way that the theory remains free of anomalies and general relativity is recovered for $\lambda=0$. In addition, the corresponding metric is constructed in a fully covariant way to ensure that gauge transformations on phase space correspond to coordinate changes. The solution for each gauge choice provides a chart and corresponding line element of a spacetime solution whose geometry is unambiguously determined in terms of the parameter $\lambda$ and a constant of motion $m$. For positive values of $m$, the solution is asymptotically flat and contains a globally hyperbolic black-hole/white-hole region with a minimal spacelike hypersurface that replaces the Schwarzschild singularity. The corresponding exterior regions are isometric and, in particular, allow the computation of the ADM mass. The procedure to obtain the global causal structure of the solution yields also its maximal analytic extension.