Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class

TL;DR

This paper explores higher-dimensional Robinson-Trautman spacetimes with p-form Maxwell fields, revealing diverse static and dynamic black hole solutions influenced by the dimension and form degree, including special cases with self-dual fields.

Contribution

It classifies exact Robinson-Trautman solutions with p-form fields in higher dimensions, highlighting new static and non-static black hole configurations based on dimension and form degree.

Findings

Odd dimensions yield static black holes with Einstein horizon spaces.

Even dimensions allow dynamic solutions with mass change via electromagnetic radiation.

Conditions for self-dual Maxwell fields are identified and explicit examples provided.

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 by an electric and a magnetic field and whose horizon is an Einstein space (further constrained by the Einstein-Maxwell equations) -- both the Weyl and Maxwell type are D. Even dimensions, however, open up more possibilities. In particular, when 2p=n there exist non-static solutions describing black holes acquiring (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.