On the causal characterization of singularities in spherically symmetric spacetimes

TL;DR

This paper investigates the causal nature of singularities at zero areal radius in spherically symmetric spacetimes, using qualitative dynamic systems techniques, and explores implications for black hole evaporation and cosmic censorship.

Contribution

It introduces a comprehensive scheme to determine the causal character of R=0 singularities based on the scalar invariant m, advancing understanding of singularity outcomes in gravitational collapse.

Findings

Persistent naked singularities may form during black hole evaporation.

The scalar invariant m suffices to characterize singularity causality.

Naked singularities could arise from stellar collapse, challenging cosmic censorship.

Abstract

The causal character of the zero-areal-radius (R=0) singularity in spherically symmetric spacetimes is studied. By using the techniques of the qualitative behaviour of dynamic systems, we are able to present the most comprehensive scheme so far to try to find out their causal characterization, taking into account and analyzing, the possible limitations of the approach. We show that, with this approach, the knowledge of the scalar invariant $m\equiv R(1-g^{\mu\nu}\partial_\mu R\partial_\nu R)/2$ suffices to characterize the singularity. We apply our results to the study of the outcome of Black Hole evaporation and show different possibilities. In this way, we find that a persistent naked singularity could develop in the final stages of the evaporation and we show its distinctive features. Likewise, we study the options for the generation of naked singularities in the collapse of an object (such as a star) as a means of violating the cosmic censorship conjecture.