TY  - JOUR
A1  - Schmidt, Hans-Jürgen
A1  - Singleton, Douglas
T1  - Exact radial solution in 2+1 gravity with a real scalar field
JF  - Physics letters : B
N2  - In this Letter 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.
KW  - (2+1)-dimensional gravity
KW  - Exact solution
KW  - BTZ black hole
KW  - Self-interacting scalar field
Y1  - 2013
U6  - https://doi.org/10.1016/j.physletb.2013.03.007
SN  - 0370-2693
VL  - 721
IS  - 4-5
SP  - 294
EP  - 298
PB  - Elsevier
CY  - Amsterdam
ER  -