Supersymmetry, attractors and cosmic censorship

TL;DR

This paper demonstrates that unbroken supersymmetry in N=2 supergravity solutions generally prevents naked singularities, formulates conditions for global supersymmetry, and relates these to physical properties like absence of NUT charge and scalar hair.

Contribution

It introduces three specific conditions ensuring global supersymmetry in black-hole solutions, linking them to physical attributes and microscopic string theory interpretations.

Findings

Supersymmetric solutions generally lack naked singularities.

Explicit conditions relate supersymmetry to absence of NUT charge, angular momentum, scalar hair, and negative energy.

Certain singular solutions like Kerr-Newman with M=|q| are not supersymmetric.

Abstract

We show that requiring unbroken supersymmetry everywhere in black-hole-type solutions of N=2,d=4 supergravity coupled to vector supermultiplets ensures in most cases absence of naked singularities. We formulate three specific conditions which we argue are equivalent to the requirement of global supersymmetry. These three conditions can be related to absence of sources of NUT charge, angular momentum, scalar hair and negative energy, although the solutions can still have globally defined angular momentum and non-trivial scalar fields, as we show in an explicit example. Furthermore, only the solutions satisfying these requirements seem to have a microscopic interpretation in String Theory since only they have supersymmetric sources. These conditions exclude, for instance, singular solutions such as the Kerr-Newman with M=|q|, which fails to be everywhere supersymmetric. We also present a re-derivation of several results concerning attractors in N=2,d=4 theories based in the explicit knowledge of the most general solutions of the timelike class.