Supersymmetric Black Holes

TL;DR

This paper demonstrates that certain supersymmetric black hole solutions in N=2, d=4 supergravity are exact and unaffected by quantum corrections, highlighting their stability and special properties in supersymmetric backgrounds.

Contribution

It identifies and constructs manifestly supersymmetric black hole solutions that remain exact solutions even with quantum supergravity corrections.

Findings

Quantum corrections do not alter the effective action in specific supersymmetric backgrounds.

Supersymmetric black holes can be described as solutions of flatness conditions in superspace.

Constructed solutions include extremal Reissner-Nordstr"om black holes with unbroken supersymmetries.

Abstract

The effective action of $N=2$, $d=4$ supergravity is shown to acquire no quantum corrections in background metrics admitting super-covariantly constant spinors. In particular, these metrics include the Robinson-Bertotti metric (product of two 2-dimensional spaces of constant curvature) with all 8 supersymmetries unbroken. Another example is a set of arbitrary number of extreme Reissner-Nordstr\"om black holes. These black holes break 4 of 8 supersymmetries, leaving the other 4 unbroken. We have found manifestly supersymmetric black holes, which are non-trivial solutions of the flatness condition $\cd^{2} = 0$ of the corresponding (shortened) superspace. Their bosonic part describes a set of extreme Reissner-Nordstr\"om black holes. The super black hole solutions are exact even when all quantum supergravity corrections are taken into account.