Cosmic Censorship and the Evolution of d-Dimensional Charged Evaporating Black Holes

TL;DR

This paper investigates whether Hawking evaporation can violate cosmic censorship in higher-dimensional charged black holes, concluding that it cannot and that reaching extremality becomes harder as dimensions increase.

Contribution

The study generalizes the Hiscock and Weems model to higher dimensions, showing Hawking evaporation does not violate cosmic censorship in d-dimensional Reissner-Nordstr"om black holes.

Findings

Hawking evaporation does not lead to cosmic censorship violation in higher dimensions.

Reaching extremality becomes more difficult as the number of dimensions increases.

Cosmic censorship remains valid under Hawking emission in all considered dimensions.

Abstract

The cosmic censorship conjecture essentially states that naked singularities should not form from generic initial conditions. Since black hole parameters can change their values under Hawking evaporation, one has to ask whether it is possible to reach extremality by simply waiting for the black hole to evaporate. If so a slight perturbation would likely render the singularity naked. Fortunately, at least for the case of asymptotically flat 4-dimensional Reissner-Nordstr\"om black hole, Hiscock and Weems showed that it can never reach extremality despite the fact that for a sufficiently massive black hole, its charge-to-mass ratio can increase during Hawking evaporation. Hence cosmic censorship is never violated by Hawking emission. However, we know that under some processes, it is easier to violate cosmic censorship in higher dimensions, therefore it is crucial to generalize Hiscock and Weems model to dimensions above four to check cosmic censorship. We found that Hawking evaporation cannot lead to violation of cosmic censorship even in higher dimensional Reissner-Nordstr\"om spacetimes. Morerover, it seems to be more difficult to reach extremality as number of dimension increases.