Central charges, black-hole entropy and geometrical structure of N-extended supergravities in D=4

TL;DR

This paper derives moduli-independent U-invariants for N>2 extended supergravities in four dimensions, providing a universal topological entropy formula for extremal black holes that relates to central charges and black-hole mass.

Contribution

It introduces a general method to define absolute U-invariants in extended supergravities, linking black-hole entropy to central charges and geometric structures.

Findings

Derived explicit U-invariants for N>2 supergravities

Connected invariants to Bekenstein-Hawking entropy formula

Showed invariants reduce to black-hole mass for fixed scalars

Abstract

The derivation of absolute (moduli-independent) U-invariants for all N>2 extended supergravities at D=4 in terms of (moduli-dependent) central and matter charges is reported. These invariants give a general definition of the ``topological'' Bekenstein-Hawking entropy formula for extremal black-holes and reduce to the square of the black-hole ADM mass for ``fixed scalars'' which extremize the black-hole ``potential'' energy.