Non-extremal Black Holes, Harmonic Functions, and Attractor Equations

TL;DR

This paper introduces a method to deform extremal black hole solutions into non-extremal ones across various Einstein-Vector-Scalar theories, preserving scalar attractor equations and providing explicit solutions for certain models.

Contribution

It presents a largely matter-sector independent deformation technique for extremal black holes into non-extremal solutions, maintaining scalar attractor equations.

Findings

Deformation method applies to a wide class of theories.

Scalar attractor equations remain unchanged under deformation.

Explicit solutions found for the five-dimensional STU-model.

Abstract

We present a method which allows to deform extremal black hole solutions into non-extremal solutions, for a large class of supersymmetric and non-supersymmetric Einstein-Vector-Scalar type theories. The deformation is shown to be largely independent of the details of the matter sector. While the line element is dressed with an additional harmonic function, the attractor equations for the scalars remain unmodified in suitable coordinates, and the values of the scalar fields on the outer and inner horizon are obtained from their fixed point values by making specific substitutions for the charges. For a subclass of models, which includes the five-dimensional STU-model, we find explicit solutions.