Supersymmetry as a Cosmic Censor

TL;DR

This paper establishes a deep link between supersymmetry and cosmic censorship for dilaton black holes in N=4 supergravity/string theory. By embedding (U(1))^2 dilaton black holes into a SUSY framework, it identifies two central charges z1 and z2 and shows extremal solutions saturate M≥|z1|, M≥|z2|, with specific SUSY preserved depending on electric/magnetic charge configuration. It analyzes thermodynamic properties near extremality, showing zero temperature for many extremal cases while maintaining nonzero entropy, and proves a nonrenormalization theorem ensuring the extreme black hole partition function receives no quantum corrections in both Lorentzian and Euclidean signatures. The work culminates in a Super Cosmic Censorship idea: SUSY bounds shield naked singularities, and multi-hole extremes can equilibrate without violating fundamental quantum principles, with intriguing implications for black hole evaporation and quantum gravity.

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-Nordström 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 $2π|PQ|$. 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.