Quantum Collapse of a Charged $n$-dimensional BTZ-like Domain Wall

Abstract

We investigate both the classical and quantum gravitational collapse of a charged, non-rotating $n$-dimensional BTZ black hole in AdS space. This is done by first deriving the conserved mass of a "spherically" symmetric domain wall, which is then taken as the classical Hamiltonian of the domain wall. In the classical picture, we show that, as far as the asymptotic observer is concerned, the details of the collapse depend on the amount of charge present in the domain wall. In the both the extremal and non-extremal cases, the collapse takes an infinite amount of observer time to complete. However, in the over-charged case, the collapse never actually occurs, instead one finds an oscillatory solution which prevents the formation of a naked singularity. As far as the infalling observer is concerned, the collapse is completed within a finite amount of proper time. Thus, the gravitational collapse follows that of the typical formation of a black hole via gravitational collapse. Quantum mechanically, in the absence of induced quasi-particle production and fluctuations of the metric geometry, we take primary interest in the behavior of the collapse near the horizon and near the classical singularity from the point of view of both asymptotic and infalling observers. For the asymptotic observer, we find that quantum effects near the horizon do not change the classical conclusions. For the infalling observer, the most interesting quantum mechanical effect are when the collapsing shell approaches the classical singularity. Here, we find, that the quantum effects in this region display non-local effects, which depend on the energy density of the domain wall.