Rotating, inhomogeneous dust interior for the BTZ black hole
Abstract
We present exact solutions describing rotating, inhomogeneous dust with generic initial data in 2+1 dimensional anti-de Sitter space-time and show how they are smoothly matched to the Banados-Teitelboim-Zanelli (BTZ) solution in the exterior. The metrics, which are the rotational analogues of the 2+1 dimensional LeMaitre-Tolman-Bondi family, are described by their angular momentum and one additional constant which, together with the angular momentum, determines the energy density of the dust cloud. The weak energy condition gives a constraint on the angular momentum profile inside the cloud. Solutions can be stationary or time dependent, but only the time-dependent solutions can be matched consistently to a BTZ exterior. No singularity is formed in either the stationary or the time-dependent cases.
- Publication:
-
Physical Review D
- Pub Date:
- July 2008
- DOI:
- 10.1103/PhysRevD.78.024038
- arXiv:
- arXiv:0805.1908
- Bibcode:
- 2008PhRvD..78b4038V
- Keywords:
-
- 04.20.Jb;
- 04.60.Kz;
- 04.70.Bw;
- Exact solutions;
- Lower dimensional models;
- minisuperspace models;
- Classical black holes;
- General Relativity and Quantum Cosmology;
- Astrophysics;
- High Energy Physics - Theory
- E-Print:
- 16 pages, no figures