Supersymmetry and attractors
Abstract
We find a general principle which allows one to compute the area of the horizon of N=2 extremal black holes as an extremum of the central charge. One considers the ADM mass equal to the central charge as a function of electric and magnetic charges and moduli and extremizes this function in the moduli space (a minimum corresponds to a fixed point of attraction). The extremal value of the square of the central charge provides the area of the horizon, which depends only on electric and magnetic charges. The doubling of unbroken supersymmetry at the fixed point of attraction for N=2 black holes near the horizon is derived via conformal flatness of the BertottiRobinsontype geometry. These results provide an explicit modelindependent expression for the macroscopic BekensteinHawking entropy of N=2 black holes which is manifestly duality invariant. The presence of hypermultiplets in the solution does not affect the area formula. Various examples of the general formula are displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the relation to the N=2 case. The entropyarea formula in five dimensions, recently discussed in the literature, is also seen to be obtained by extremizing the 5d central charge.
 Publication:

Physical Review D
 Pub Date:
 July 1996
 DOI:
 10.1103/PhysRevD.54.1514
 arXiv:
 arXiv:hepth/9602136
 Bibcode:
 1996PhRvD..54.1514F
 Keywords:

 04.65.+e;
 04.70.Dy;
 11.25.Mj;
 11.20.Pb;
 Supergravity;
 Quantum aspects of black holes evaporation thermodynamics;
 Compactification and fourdimensional models;
 High Energy Physics  Theory
 EPrint:
 20 pages, 2 figures, LaTeX. few misprints removed, version to appear in Phys. Rev. D