Non-extremal black holes from the generalised r-map

TL;DR

This paper explores the dimensional reduction of five-dimensional theories to construct and analyze non-extremal black hole solutions, providing explicit solutions for certain models and criteria for lifting instantons to black holes.

Contribution

It generalizes the r-map for 5D supergravity, explicitly solves equations for STU-like models, and identifies conditions for lifting solutions to five-dimensional black holes.

Findings

Explicit solutions for STU-like models.

Restricted solutions for block diagonal models.

Conditions for finite horizon scalar fields.

Abstract

We review the timelike dimensional reduction of a class of five-dimensional theories that generalises 5D, N = 2 supergravity coupled to vector multiplets. As an application we construct instanton solutions to the four-dimensional Euclidean theory, and investigate the criteria for solutions to lift to static non-extremal black holes in five dimensions. We focus specifically on two classes of models: STU-like models, and models with a block diagonal target space metric. For STU-like models the second order equations of motion of the four-dimensional theory can be solved explicitly, and we obtain the general solution. For block diagonal models we find a restricted class of solutions, where the number of independent scalar fields depends on the number of blocks. When lifting these solutions to five dimensions we show, by explicit calculation, that one obtains static non-extremal black holes with scalar fields that take finite values on the horizon only if the number of integration constants reduces by exactly half.