Relating black holes in two and three dimensions

TL;DR

This paper explores how three-dimensional BTZ black holes can be reduced to two-dimensional models, revealing new black hole solutions and connections to string-inspired gravity, aiding in the study of quantum scattering.

Contribution

It introduces various dimensional reduction methods of BTZ black holes to two-dimensional gravity models, providing new solutions and insights into their properties.

Findings

Derived two-dimensional black hole solutions from BTZ black holes.

Connected BTZ solutions to the two-dimensional black hole and linear dilaton vacuum.

Provided models suitable for studying exact S-wave scattering.

Abstract

The three dimensional black hole solutions of Ba\~nados, Teitelboim and Zanelli (BTZ) are dimensionally reduced in various different ways. Solutions are obtained to the Jackiw-Teitelboim theory of two dimensional gravity for spinless BTZ black holes, and to a simple extension with a non-zero dilaton potential for black holes of fixed spin. Similar reductions are given for charged black holes. The resulting two dimensional solutions are themselves black holes, and are appropriate for investigating exact ``S-wave'' scattering in the BTZ metrics. Using a different dimensional reduction to the string inspired model of two dimensional gravity, the BTZ solutions are related to the familiar two dimensional black hole and the linear dilaton vacuum.