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 it 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 hyperboloid in a 5D Minkowski spacetime, and on the physics of the strut. We also comment the cases A = 1/l and A < 1/l that represent, a single accelerated black hole in the AdS background. The C-metric is all exact solution which includes a radiative term and describes the final state of quantum pair creation of black holes.