Supersymmetry of the Robinson-Trautman solution

TL;DR

This paper classifies supersymmetric Robinson-Trautman solutions within four-dimensional ${ m N}=2$ gauged supergravity, revealing their explicit forms and singularity properties through systematic analysis of Killing spinor equations.

Contribution

It provides the first exhaustive classification of supersymmetric Robinson-Trautman spacetimes in this supergravity context, including explicit metric and spinor solutions.

Findings

Supersymmetric Robinson-Trautman solutions are generally singular.

Explicit forms of Killing spinors are derived.

The classification is systematic and comprehensive.

Abstract

The Robinson-Trautman solution in the Einstein-Maxwell-$\Lambda$ system admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. Restricting to the case where the Maxwell field is aligned, i.e., the spacetime is algebraically special, we provide an exhaustive classification of supersymmetric Robinson-Trautman spacetimes in the four-dimensional ${\cal N}=2$ gauged supergravity. The differential constraints that arise from the integrability conditions of the Killing spinor equation enable us to systematically reconstruct the metric. We derive the explicit form of the Killing spinor either by directly integrating the Killing spinor equation or by casting the solution into the canonical form of supersymmetric solutions given in hep-th/0307022. In any case, the supersymmetric Robinson-Trautman solution generically exhibits a naked singularity.