Accelerating black diholes and static black di-rings

We show how a recently discovered black ring solution with a rotating 2-sphere can be turned into two new solutions of Einstein–Maxwell–dilaton theory. The first is a four-dimensional solution describing a pair of oppositely charged, extremal black holes—known as a black dihole—undergoing uniform acceleration. The second is a five-dimensional solution describing a pair of concentric, static extremal black rings carrying opposite dipole charges—a so-called black di-ring. The properties of both solutions, which turn out to be formally very similar, are analyzed in detail. We also present, in an appendix, an accelerating version of the Zipoy–Voorhees solution in four-dimensional Einstein gravity.