Static and radiating dyonic black holes coupled to conformally invariant electrodynamics in higher dimensions

Abstract

We investigate the complete family of (aligned) Robinson-Trautman spacetimes sourced by conformally invariant non-linear electrodynamics in $D$ dimensions in the presence of an arbitrary cosmological constant. After presenting general features of the solutions (which exist only in even dimensions), we discuss in more detail some particular subclasses. Static metrics contain dyonic black holes with various possible horizon geometries (K\"ahler if there is a magnetic field, including flat branes) and different asymptotics. In addition, there exist also time-dependent solutions (not possible in the $D>4$ linear theory) which may represent white hole evaporation by emission of electromagnetic radiation (or a time-reversed picture of black hole formation). For those, we comment on a quasi-local characterization of possible past horizons. Finally, we briefly discuss the special case of stealth solutions. In an appendix, a theory-independent result on the redundancy of the gravity part of the field equations for Robinson-Trautman spacetimes is further obtained.