Testing Cosmic Censorship with Black Hole Collisions

TL;DR

This paper investigates black hole collisions with total mass exceeding the extremal limit in a universe with positive cosmological constant, revealing conditions under which naked singularities form and discussing implications for cosmic censorship.

Contribution

It introduces an exact solution for colliding black holes with $ ext{Q}=M$ and $ ext{}\Lambda>0$, analyzing the global structure and singularity formation.

Findings

Naked singularities form when total mass exceeds the extremal limit.

The horizon in such collisions is not smooth and has a mild curvature singularity.

Geodesics can still be extended despite the singularity.

Abstract

There exists an upper limit on the mass of black holes when the cosmological constant $\Lambda$ is positive. We study the collision of two black holes whose total mass exceeds this limit. Our investigation is based on a recently discovered exact solution describing the collision of $Q=M$ black holes with $\Lambda > 0$. The global structure of this solution is analyzed. We find that if the total mass is less than the extremal limit, then the black holes coalesce. If it is greater, then a naked singularity forms to the future of a Cauchy horizon. However, the horizon is not smooth. Generically, there is a mild curvature singularity, which still allows geodesics to be extended. The implications of these results for cosmic censorship are discussed.