A Rotating, Inhomogeneous Dust Interior for the BTZ Black Hole

TL;DR

This paper derives exact, inhomogeneous, rotating dust solutions in 2+1 AdS spacetime, matching them smoothly to BTZ black holes without forming singularities, and explores their properties and constraints.

Contribution

It introduces new rotating, inhomogeneous dust solutions in 2+1 AdS spacetime that extend the LTB family and are compatible with BTZ exterior solutions.

Findings

Time-dependent solutions can be matched to BTZ exterior

No singularities are formed in the solutions

Weak energy condition constrains angular momentum profile

Abstract

We present exact solutions describing rotating, inhomogeneous dust with generic initial data in 2+1 dimensional AdS spacetime 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 (LTB) 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.