U-Invariants, Black-Hole Entropy and Fixed Scalars

Details U-Invariants, Black-Hole Entropy and Fixed Scalars U-Invariants, Black-Hole Entropy and Fixed Scalars

1997-03-23

arxiv.org/abs/hep-th/9703156v1

Phys.Lett. B403 (1997) 12-19

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX, no figures

Scientific paper

10.1016/S0370-2693(97)00454-1

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.

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