Static and radiating p-form black holes in the higher dimensional robinson-trautman class

Abstract

We study Robinson-Trautman spacetimes in the presence of an aligned p-form Maxwell field and an arbitrary cosmological constant in n ≥ 4 dimensions. As it turns out, the character of these exact solutions depends significantly on the (relative) value of n and p. In odd dimensions the solutions reduce to static black holes dressed with an electric and a magnetic field, with an Einstein space horizon (further constrained by the Einstein-Maxwell equations) — both the Weyl and Maxwell types are D. Even dimensions, however, open up more possibilities. In particular, when 2p = n there exist non-static solutions describing black holes gaining (or losing) mass by receiving (or emitting) electromagnetic radiation. In this case the Weyl type is II (D) and the Maxwell type can be II (D) or N. Conditions under which the Maxwell field is self-dual (for odd p) are also discussed, and a few explicit examples presented. Finally, the case p = 1 is special in all dimensions and leads to static metrics with a non-Einstein transverse space.