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

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