Universality of Sypersymmetric Attractors

Abstract

The macroscopic entropy-area formula for supersymmetric black holes in N=2,4,8 theories is found to be universal: in d=4 it is always given by the square of the largest of the central charges extremized in the moduli space. The proof of universality is based on the fact that the doubling of unbroken supersymmetry near the black hole horizon requires that all central charges other than Z=M vanish at the attractor point for N=4,8. The ADM mass at the extremum can be computed in terms of duality symmetric quartic invariants which are moduli independent. The extension of these results for d=5, N=1,2,4 is also reported. A duality symmetric expression for the energy of the ground state with spontaneous breaking of supersymmetry is provided by the power 1/2 (2/3) of the black hole area of the horizon in d=4 (d=5). It is suggested that the universal duality symmetric formula for the energy of the ground state in supersymmetric gravity is given by the modulus of the maximal central charge at the attractor point in any supersymmetric theory in any dimension.Comment: few misprints removed, version to appear in Phys. Rev. 20 pages, 1 figur