Duality, Central Charges and Entropy of Extremal BPS Black Holes

TL;DR

This paper derives a duality-invariant entropy formula for extremal BPS black holes in higher-dimensional supergravity, classifies solutions based on supersymmetry preservation, and discusses implications in string and M-theory.

Contribution

It presents a new duality-invariant entropy formula for all N>2 supergravities and classifies BPS black holes using U-duality orbits of exceptional groups.

Findings

Derived a universal entropy formula invariant under duality transformations.

Classified BPS black holes by supersymmetry fractions and U-duality orbits.

Connected supergravity results with string and M-theory frameworks.

Abstract

We report on some general results on the physics of extremal BPS black holes in four and five dimensions. The duality-invariant entropy-formula for all $N>2$ extended supergravities is derived. Its relation with the fixed-scalar condition for the black-hole ``potential energy'' wich extremizes the BPS mass is obtained. BPS black holes preserving different fractions of supersymmetry are classified in a U-duality invariant set up. The latter deals with different orbits of the fundamental representations of the exceptional groups $E_{7(7)}$ and $E_{6(6)}$. We comment upon the interpretation of these results in a string and M-theory framework.