Black Holes in Two Dimensions

Yuri N. Obukhov, Friedrich W. Hehl

Published 1998-07-14Version 1

Models of black holes in (1+1)-dimensions provide a theoretical laboratory for the study of semi-classical effects of realistic black holes in Einstein's theory. Important examples of two-dimensional models are given by string theory motivated dilaton gravity, by ordinary general relativity in the case of spherical symmetry, and by {\em Poincar\'e gauge gravity} in two spacetime dimensions. In this paper, we present an introductory overview of the exact solutions of two-dimensional classical Poincar\'e gauge gravity (PGG). A general method is described with the help of which the gravitational field equations are solved for an arbitrary Lagrangian. The specific choice of a torsion-related coframe plays a central role in this approach. Complete integrability of the general PGG model is demonstrated in vacuum, and the structure of the black hole type solutions of the quadratic models with and without matter is analyzed in detail. Finally, the integrability of the general dilaton gravity model is established by recasting it into an effective PGG model.