Supersymmetry, attractors and cosmic censorship

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 the absence of sources for 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 on the explicit knowledge of the most general solutions in the timelike class.

Supersymmetry and cosmic censorship

“…In particular we have a KSI of the form [27] E m0 = − √ The metrics of all supersymmetric black holes and rings are of the form [28,29,30] …”

“…The explicit knowledge of the most general supersymmetric black-hole-type solutions of N = 2, d = 4 SUGRA theories [13,14] has led as to reformulate the 1992 conjecture extending the requirement of supersymmetry to the sources that give rise to the macroscopic fields [15]. The conjecture says now that supersymmetric, asymptotically-flat, black-holetype solutions satisfying the following conditions will be regular black holes without naked singularities:…”

All the timelike supersymmetric solutions of all ungauged d = 4 supergravities

“…[13,36] for N = 2 theories coupled to vector multiplets and with the same integrability condition, namely…”

Supersymmetric non‐Abelian black holes and monopoles in Einstein‐Yang‐Mills SUGRAs

“…Unsurprisingly, not every choice for the seed functions leads to a regular black hole spacetime, but the necessary and sufficient conditions that allow for a static, asymptotically flat, spherically symmetric black hole are known (see e.g. [2]). Apart from the absence of NUT charge and the positivity of the ADM mass, the only remaining condition one has to impose is the existence of a horizon.…”

“…As the metric G is Kähler it can be derived from a Kähler potential, K, which for the chosen model reads e −K = 1 − |Z| 2 . Observe that the Kähler potential imposes the constraint 0 ≤ |Z| 2 ≤ 1, but it can be shown that a BH solution automatically satisfies this bound [2]. The explicit form of the complex matrix N and the potential V , which by construction is positive semi-definite, can be written down, but as they will not be used we shall refrain from doing it.…”