Modified Black Holes in Two Dimensional Gravity

TL;DR

This paper explores modifications to two-dimensional black hole solutions in the $SL(2,R)/U(1)$ model by adding a topological term, revealing new singularities and interpreting the term as a conformal perturbation.

Contribution

It introduces a topological term into the $SL(2,R)/U(1)$ model, analyzing its effects on geometry and black hole solutions, and interprets it as a conformal perturbation.

Findings

The geometry exhibits new singularities beyond the known black hole.

The topological term can be viewed as a (1,1) conformal operator perturbation.

Special cases recover the standard black hole solutions.

Abstract

The $SL(2,R)/U(1)$ gauged WZWN model is modified by a topological term and the accompanying change in the geometry of the two dimensional target space is determined. The possibility of this additional term arises from a symmetry in the general formalism of gauging an isometry subgroup of a non-linear sigma model with an antisymmetric tensor. It is shown, in particular, that the space-time exhibits some general singularities for which the recently found black hole is just a special case. From a conformal field theory point of view and for special values of the unitary representations of $SL(2,R)$, this topological term can be interpreted as a small perturbation by a (1,1) conformal operator of the gauged WZWN action.