Special geometry, black holes and Euclidean supersymmetry

TL;DR

This paper reviews recent advances in special geometry and its application to supersymmetric black holes, including Euclidean versions, and discusses how these mathematical structures help analyze black hole solutions.

Contribution

It provides a comprehensive overview of special geometry, including para-complex structures in Euclidean supersymmetry, and explains their role in studying black hole solutions.

Findings

Summarizes the role of special geometry in supersymmetric black holes

Explains para-complex special geometry in Euclidean supersymmetry

Illustrates the use of real coordinates and dimensional reduction in black hole analysis

Abstract

We review recent developments in special geometry and explain its role in the theory of supersymmetric black holes. To make this article self-contained, a short introduction to black holes is given, with emphasis on the laws of black hole mechanics and black hole entropy. We also summarize the existing results on the para-complex version of special geometry, which occurs in Euclidean supersymmetry. The role of real coordinates in special geometry is illustrated, and we briefly indicate how Euclidean supersymmetry can be used to study stationary black hole solutions via dimensional reduction over time. This article is an updated and substantially extended version of the previous review article `New developments in special geometry', hep-th/0602171.