Rotating Dilaton Black Holes

TL;DR

This paper investigates rotating black hole solutions in a system combining gravity, electromagnetism, and a dilaton field, revealing special cases where rotation can be generated from non-rotating solutions due to enhanced symmetries.

Contribution

It identifies the conditions under which rotating solutions can be generated from non-rotating ones in dilaton black hole systems, highlighting the role of target space symmetries for specific dilaton couplings.

Findings

Rotating solutions are only generated for specific dilaton couplings a=0, ±√3.

Target space symmetry is enlarged at these special coupling values.

New solutions are constructed using symmetry transformations.

Abstract

We consider the axially symmetric coupled system of gravitation, electromagnetism and a dilaton field. Reducing from four to three dimensions, the system is described by gravity coupled to a non-linear $\sigma$-model. We find the target space isometries and use them to generate new solutions. It seems that it is only possible to generate rotating solutions from non-rotating ones for the special cases when the dilaton coupling parameter $a=0, \pm \sqrt{3}$. For those particular values, the target space symmetry is enlarged.