Non-extremal black hole solutions from the c-map

TL;DR

This paper develops a systematic method to construct non-extremal black hole solutions in four-dimensional ${ m N}=2$ supergravity using the c-map and special geometry, providing new explicit solutions and insights into their properties.

Contribution

It introduces a novel systematic approach for deriving non-extremal black hole solutions in ${ m N}=2$ supergravity, including the full solutions for certain models and partial solutions for others.

Findings

Explicit non-extremal black hole solutions for specific models.

Regularity conditions halve the number of free parameters.

Identification of a set of first order equations for these solutions.

Abstract

We construct new static, spherically symmetric non-extremal black hole solutions of four-dimensional ${\cal N}=2$ supergravity, using a systematic technique based on dimensional reduction over time (the c-map) and the real formulation of special geometry. For a certain class of models we actually obtain the general solution to the full second order equations of motion, whilst for other classes of models, such as those obtainable by dimensional reduction from five dimensions, heterotic tree-level models, and type-II Calabi-Yau compactifications in the large volume limit a partial set of solutions are found. When considering specifically non-extremal black hole solutions we find that regularity conditions reduce the number of integration constants by one half. Such solutions satisfy a unique set of first order equations, which we identify. Several models are investigated in detail, including examples of non-homogeneous spaces such as the quantum deformed $STU$ model. Though we focus on static, spherically symmetric solutions of ungauged supergravity, the method is adaptable to other types of solutions and to gauged supergravity.