Black holes without spacelike singularities

TL;DR

This paper demonstrates that small perturbations of Reissner-Nordström black holes can lead to spacetimes without spacelike singularities, with the boundary represented by a bifurcate null hypersurface where the metric extends continuously but not smoothly.

Contribution

It shows that under certain conditions, the boundary of the evolving spacetime is a bifurcate null hypersurface with no spacelike singularities, extending previous results to a broader class of perturbations.

Findings

Hawking mass blows up along the null hypersurface

The metric extends continuously but not twice differentiably

No spacelike component of singularity in an open set of solutions

Abstract

It is shown that for small, spherically symmetric perturbations of asymptotically flat two-ended Reissner-Nordstr\"om data for the Einstein-Maxwell-real scalar field system, the boundary of the dynamic spacetime which evolves is globally represented by a bifurcate null hypersurface across which the metric extends continuously. Under additional assumptions, it is shown that the Hawking mass blows up identically along this bifurcate null hypersurface, and thus the metric cannot be extended twice differentiably, in fact, cannot be extended in a weaker sense characterized at the level of the Christoffel symbols. The proof combines estimates obtained in previous work with an elementary Cauchy stability argument. There are no restrictions on the size of the support of the scalar field, and the result applies to both the future and past boundary of spacetime. In particular, it follows that for an open set in the moduli space of solutions around Reissner-Nordstr\"om, there is no spacelike component of either the future or the past singularity.