Supersymmetry as a Cosmic Censor

TL;DR

This paper demonstrates that supersymmetry imposes bounds on charged dilaton black holes that prevent naked singularities, linking cosmic censorship to supersymmetric positivity bounds and analyzing their thermodynamic properties.

Contribution

It establishes that extreme dilaton black holes saturate supersymmetry bounds, ensuring cosmic censorship and extending the understanding of black hole stability in supersymmetric theories.

Findings

Extreme dilaton black holes admit super-covariantly constant spinors.

The supersymmetric positivity bound prevents naked singularities.

Extreme black holes cannot evaporate without violating supersymmetry bounds.

Abstract

In supersymmetric theories the mass of any state is bounded below by the values of some of its charges. The corresponding bounds in case of Schwarzschild and Reissner-Nordstr\"om black holes are known to coincide with the requirement that naked singularities be absent. Here we investigate charged dilaton black holes in this context. We show that the extreme solutions 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 super-covariantly constant spinors. The supersymmetric positivity bound for dilaton black holes, $M \geq \frac{1}{\sqrt 2}(|Q|+|P|)$, takes care of the absence of naked singularities of the dilaton black holes and is, in this sense, equivalent to the cosmic censorship condition. The temperature, entropy and singularity are discussed. The Euclidean action (entropy) of the extreme black hole is given by $2\pi |PQ|$. We argue that this result, as well as the one for Lorentzian signature, is not altered by higher order corrections in the supersymmetric theory. When a black hole reaches its extreme limit, it cannot continue to evaporate by emitting 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.