Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions

TL;DR

This paper derives and classifies higher-dimensional Robinson-Trautman spacetimes with electromagnetic fields, revealing their relation to known black hole solutions and extending the understanding of Einstein-Maxwell solutions in various dimensions.

Contribution

It provides the complete family of solutions for higher-dimensional Robinson-Trautman spacetimes with electromagnetic fields, including new parameters and conditions for different dimensions.

Findings

In odd dimensions, solutions are generalized Reissner-Nordstrom-de Sitter black holes.

Event horizons can be Einstein spaces with parameters for mass, charge, and cosmological constant.

Solutions include magnetic monopole-like parameters in even dimensions with (almost-)Kahler Einstein transverse spaces.

Abstract

We investigate higher dimensional Robinson-Trautman spacetimes with an electromagnetic field aligned with the hypersurface orthogonal, non-shearing, expanding geodesic null congruence. After integrating the system of Einstein-Maxwell equations with an arbitrary cosmological constant, we present the complete family of solutions. In odd spacetime dimensions they represent (generalized) Reissner-Nordstrom-de Sitter black holes. The event horizon (more generically, the transverse space) may be any Einstein space, and the full metric is specified by three independent parameters related to mass, electric charge and cosmological constant. These solutions also exhaust the class of Robinson-Trautman spacetimes with an aligned Maxwell-Chern-Simons field (the CS term must vanish because of the alignment assumption and of the Einstein equations). In even dimensions an additional magnetic "monopole-like" parameter is also allowed provided now the transverse space is an (almost-)Kahler Einstein manifold. The Weyl tensor of all such solutions is of algebraic type D. We also consider the possible inclusion of aligned pure radiation.