Higher dimensional Robinson-Trautman spacetimes sourced by p-forms: static and radiating black holes

TL;DR

This paper explores higher-dimensional Robinson-Trautman spacetimes with p-form fields, revealing static black holes in odd dimensions and radiating black holes in even dimensions, with implications for their electromagnetic properties and Weyl types.

Contribution

It provides a unified analysis of Robinson-Trautman solutions with p-form fields across various dimensions, highlighting conditions for static and radiating black holes.

Findings

In odd dimensions, solutions are static black holes with electromagnetic fields.

In even dimensions, solutions can describe radiating black holes gaining or losing mass.

The Weyl type of these spacetimes varies depending on the case.

Abstract

We summarize results about Robinson-Trautman spacetimes in the presence of an aligned $p$-form Maxwell field and an arbitrary cosmological constant in $n\ge 4$ dimensions. While in odd dimensions the solutions reduce to static black holes dressed with an electric and a magnetic field (with an Einstein space horizon), in even dimensions $2p=n$ they may also describe black holes gaining (or losing) mass by receiving (or emitting) electromagnetic radiation. The Weyl type of the spacetimes is also briefly discussed in all the possible cases.