Gravitational perturbation of the BTZ black hole induced by test particles and weak cosmic censorship in AdS spacetime

TL;DR

This paper studies how test particles perturb a BTZ black hole in AdS space and confirms that the black hole cannot be overspun, supporting the weak cosmic censorship conjecture in this setting.

Contribution

It provides the first analysis of gravitational perturbations caused by test particles in a BTZ black hole within AdS space, addressing energy and angular momentum definitions.

Findings

Test particles do not overspin the BTZ black hole beyond extremality.

Confirmed the correct definitions of energy and angular momentum in AdS.

Supported the weak cosmic censorship conjecture in AdS spacetime.

Abstract

We analyze the gravitational perturbations induced by particles falling into a three dimensional, asymptotically AdS black hole geometry. More specifically, we solve the linearized perturbation equations obtained from the geodesic motion of a ring-like distribution of test particles in the BTZ background. This setup ensures that the U(1) symmetry of the background is preserved. The non-asymptotic flatness of the background raises difficulties in attributing the significance of energy and angular momentum to the conserved quantities of the test particles. This issue is well known but, to the best of our knowledge, has never been addressed in the literature. We confirm that the naive expressions for energy and angular momentum are the correct definitions. Finally, we put an asymptotically AdS version of the weak cosmic censorship to a test: by attempting to overspin the BTZ black hole with test particles it is found that the black hole cannot be spun-up past its extremal limit.