Charged rotating black holes in dilaton gravity

TL;DR

This paper constructs charged rotating black hole solutions in five-dimensional dilaton gravity with curved horizons, extending static solutions by adding small angular momentum and analyzing their properties.

Contribution

It introduces a method to obtain rotating dilaton black holes from static solutions by solving coupled differential equations, including the effects of small angular momentum.

Findings

Rotating solutions reduce to known five-dimensional black holes when dilaton is absent.

Angular momentum and velocity are computed at first order in rotation.

Solutions generalize static black holes to include rotation in dilaton gravity.

Abstract

We consider charged black holes with curved horizons, in five dimensional dilaton gravity in the presence of Liouville-type potential for the dilaton field. We show how, by solving a pair of coupled differential equations, infinitesimally small angular momentum can be added to these static solutions to obtain charged rotating dilaton black hole solutions. In the absence of dilaton field, the non-rotating version of the solution reduces to the five dimensional Reissner-Nordstr\"{o}m black hole, and the rotating version reproduces the five dimensional Kerr-Newman modification thereof for small rotation parameter. We also compute the angular momentum and the angular velocity of these rotating black holes which appear at the first order.