Exact radial solution in 2+1 gravity with a real scalar field
Abstract
In this paper we give some general considerations about circularly symmetric, static space-times in 2+1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3+1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of 2+1 dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to 2+1 dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the 2+1 dimensional character of the space-time. The solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions.
Cite
@article{arxiv.1212.1285,
title = {Exact radial solution in 2+1 gravity with a real scalar field},
author = {H. -J. Schmidt and D. Singleton},
journal= {arXiv preprint arXiv:1212.1285},
year = {2013}
}
Comments
13 pages, minor revisions, updated references, to be published PLB