Extremal Black Holes in Supergravity and the Bekenstein-Hawking Entropy

TL;DR

This paper reviews the relationship between supergravity central charges, BPS states, and black hole entropy, emphasizing the topological nature of entropy in extremal supergravity black holes and its invariance under duality transformations.

Contribution

It provides a detailed analysis of N=2 supergravity and extends the discussion to higher N theories, highlighting the topological and duality-invariant aspects of black hole entropy.

Findings

Black hole entropy is topological and moduli independent.

Entropy can be expressed using invariants of the supergravity duality group.

The study covers N=2 and N=8 supergravity cases.

Abstract

We review some results on the connection among supergravity central charges, BPS states and Bekenstein-Hawking entropy. In particular, N=2 supergravity in four dimensions is studied in detail. For higher N supergravities we just give an account of the general theory specializing the discussion to the N=8 case when one half of supersymmetry is preserved. We stress the fact that for extremal supergravity black holes the entropy formula is topological, that is the entropy turns out to be a moduli independent quantity and can be written in terms of invariants of the duality group of the supergravity theory.