Nonextremal black holes are BPS

TL;DR

This paper demonstrates that certain nonextremal black holes can be BPS solutions without being supersymmetric, challenging previous assumptions about the relationship between BPS states and supersymmetry.

Contribution

It provides counterexamples of nonextremal black holes as BPS solutions and shows they do not preserve supersymmetry, contrary to common beliefs.

Findings

Nonextremal Reissner-Nordström black holes can be BPS solutions.

These black holes do not admit generalized Killing spinors.

No supergravity theory preserves supersymmetry for these solutions.

Abstract

Extremal charged black holes are BPS solutions. It is commonly thought that their nonextremal counterparts are not. Further, experience with BPS solutions in flat spacetime suggests that all BPS solutions are supersymmetric; i.e. that they are invariant under some supersymmetry charges of either the original field theory or an appropriately extended version thereof. Using nonextremal Reissner-Nordstr\"om black holes as counterexamples, we show that neither of these expectations is universally valid. These black holes correspond to a one-parameter family of BPS solutions. By showing that, subject to one very plausible assumption, no generalized Killing spinor can be constructed for these, we show that there is no supergravity theory for which these BPS solutions preserve a fraction of the supersymmetry, nor is there an associated Witten-Nester positive energy bound.