U-Invariants, Black-Hole Entropy and Fixed Scalars

TL;DR

This paper derives moduli-independent U-invariants in extended supergravities, linking them to black-hole entropy and fixed scalars, and analyzes the properties of the black-hole potential's Hessian matrix.

Contribution

It provides explicit formulas for U-invariants in N>2 supergravities and explores their relation to black-hole entropy and the structure of the black-hole potential.

Findings

U-invariants are moduli-independent and define black-hole entropy.

At fixed scalars, the black-hole potential's Hessian is degenerate and semipositive.

The invariants reduce to the square of the ADM mass for fixed scalars.

Abstract

The absolute (moduli-independent) U-invariants of all N>2 extended supergravities at D=4 are derived in terms of (moduli-dependent) central and matter charges. 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. The Hessian matrix of the black-hole potential at ``fixed scalars'', in contrast to N=2 theories, is shown to be degenerate, with rank (N-2)(N-3) + 2 n (N being the number of supersymmetries and n the number of matter multiplets) and semipositive definite.