Pair of accelerated black holes in an anti-de Sitter background: the AdS C-metric

The anti-de Sitter C-metric (AdS C-metric) is characterized by a quite interesting new feature when compared with the C-metric in flat or de Sitter backgrounds. Indeed, contrarily to what happens in these two last exact solutions, the AdS C-metric only describes a pair of accelerated black holes if the acceleration parameter satisfies A>1/L, where L is the cosmological length. The two black holes cannot interact gravitationally and their acceleration is totally provided by the pressure exerted by a strut that pushes the black holes apart. Our analysis is based on the study of the causal structure, on the description of the solution in the AdS 4-hyperboloid in a 5D Minkowski embedding spacetime, and on the physics of the strut. We also analyze the cases A=1/L and A<1/L that represent a single accelerated black hole in the AdS background.