Strong cosmic censorship conjecture for a charged BTZ black hole

TL;DR

This paper investigates the strong cosmic censorship conjecture for charged BTZ black holes, finding that it holds in three dimensions, contrasting with violations observed in higher dimensions and rotating cases.

Contribution

It provides analytical and numerical evidence that the strong cosmic censorship conjecture is preserved for charged BTZ black holes in three dimensions, unlike in higher-dimensional or rotating black holes.

Findings

The key parameter is always less than 1/2, respecting the conjecture.

Contrasts with violations in higher dimensions and rotating BTZ black holes.

Discusses implications for photon orbit stability.

Abstract

The strong cosmic censorship conjecture, whose validation asserts the deterministic nature of general relativity, has been studied for charged BTZ black holes in three dimensional general relativity, as well as for Nth order pure Lovelock gravity in d=2N+1 spacetime dimensions. Through both analytical and numerical routes, we have computed the ratio of the imaginary part of the quasi-normal mode frequencies with the surface gravity at the Cauchy horizon. The lowest of which corresponds to the key parameter associated with violation of strong cosmic censorship conjecture. Our results demonstrate that this parameter is always less than the critical value $(1/2)$, thereby respecting the strong cosmic censorship conjecture. This is in complete contrast to the four or, higher dimensional black holes, as well as for rotating BTZ black hole, where the violation of strong cosmic censorship conjecture exists. Implications and possible connection with the stability of the photon orbits have been discussed.