The geometry of singularities and the black hole information paradox

TL;DR

This paper explores extending black hole solutions beyond singularities using advanced geometric methods, suggesting information may escape the singularity and revealing potential links to quantum gravity phenomena.

Contribution

It introduces a novel geometric approach to analytically extend black hole solutions beyond singularities, challenging the traditional view of information loss.

Findings

Black hole solutions admit extensions beyond singularities.

Information can potentially escape through these extended regions.

Spacetime exhibits dimensional reduction effects near singularities.

Abstract

The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event horizon, but at the singularity, the resulting metric is degenerate. When the metric is degenerate, the covariant derivative, the curvature, and the Einstein equation become singular. However, recent advances in the geometry of spacetimes with singular metric show that there are ways to extend analytically the Einstein equation and other field equations beyond such singularities. This means that the information can get out of the singularity. In the case of charged black holes, the obtained solutions have {\nonsing} electromagnetic field. As a bonus, if particles are such black holes, spacetime undergoes dimensional reduction effects like those required by some approaches to perturbative Quantum Gravity.