Accelerating black diholes and static black di-rings

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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.