Supersymmetry as a cosmic censor
Abstract
In supersymmetric theories the mass of any state is bounded below by the values of some of its charges. The corresponding bounds in the case of Schwarzschild (M>=0) and ReissnerNordström (M>=q) black holes are known to coincide with the requirement that naked singularities be absent. Here we investigate [U(1)]^{2} charged dilaton black holes in this context. The extreme solutions are shown to saturate the supersymmetry bound of N=4, d=4 supergravity, or dimensionally reduced superstring theory. Specifically, we have shown that extreme dilaton black holes, with electric and magnetic charges, admit supercovariantly constant spinors. The supersymmetric positivity bound for dilaton black holes is given by M>=1/ √2 (Q+P). This condition for dilaton black holes coincides with the cosmic censorship requirement that the singularities be hidden, as was the case for other asymptotically flat static blackhole solutions. We conjecture that the bounds from supersymmetry and cosmic censorship will coincide for more general solutions as well. The temperature, entropy, and singularity of the stringy black hole are discussed in connection with the extreme limit and restoration of supersymmetry. The Euclidean action (entropy) of the extreme black hole is given by 2πPQ. We argue that this result is not altered by higherorder corrections in the supersymmetric theory. In the Lorentzian signature, quantum corrections to the effective onshell action in the extreme blackhole background are also absent. When a black hole reaches its extreme limit, the thermal description breaks down. It cannot continue to evaporate by emitting (uncharged) elementary particles, since this would violate the supersymmetric positivity bound. We speculate on the possibility that an extreme black hole may ``evaporate'' by emitting smaller extreme black holes.
 Publication:

Physical Review D
 Pub Date:
 December 1992
 DOI:
 10.1103/PhysRevD.46.5278
 arXiv:
 arXiv:hepth/9205027
 Bibcode:
 1992PhRvD..46.5278K
 Keywords:

 97.60.Lf;
 04.60.+n;
 04.65.+e;
 Black holes;
 Supergravity;
 High Energy Physics  Theory
 EPrint:
 42 pages (figures not included)