Schwarzschild Singularity is Semi-Regularizable

TL;DR

This paper demonstrates that the Schwarzschild spacetime can be extended to make the singularity semi-regular and smooth, potentially allowing information to be preserved beyond the classical singularity.

Contribution

It introduces a family of analytic extensions of Schwarzschild spacetime where the singularity is degenerate and semi-regular, enabling a reformulation of field equations without infinities.

Findings

Existence of semi-regular analytic extensions of Schwarzschild spacetime

The extended solution allows the field equations to avoid infinities

Implication that information may not be destroyed at the singularity

Abstract

It is shown that the Schwarzschild spacetime can be extended so that the metric becomes analytic at the singularity. The singularity continues to exist, but it is made degenerate and smooth, and the infinities are removed by an appropriate choice of coordinates. A family of analytic extensions is found, and one of these extensions is semi-regular. A degenerate singularity doesn't destroy the topology, and when is semi-regular, it allows the field equations to be rewritten in a form which avoids the infinities, as it was shown elsewhere (arXiv:1105.0201, arXiv:1105.3404). In the new coordinates, the Schwarzschild solution extends beyond the singularity. This suggests a possibility that the information is not destroyed in the singularity, and can be restored after the evaporation.