  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.

General Relativity and Quantum Cosmology