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

Understand

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.