Equivalence principle and generalised accelerating black holes from binary systems

The Einstein equivalence principle in general relativity allows us to interpret accelerating black holes as a black hole immersed into the gravitational field of a larger companion black hole. Indeed it is demonstrated that C-metrics can be obtained as a limit of a binary system where one of the black holes grows indefinitely large, becoming a Rindler horizon. When the bigger black hole, before the limiting process, is of Schwarzschild type we recover usual accelerating black holes belonging to the Plebanski-Demianski class, thus type D. Whether the greater black hole carries some extra features, such as electric charges or rotations, we get generalised accelerating black holes which belong to a more general class, the type I. In that case the background has a richer structure, reminiscent of the physical features of the inflated companion, with respect to the standard Rindler spacetime. This insight allows us to build a general type D metric, describing an accelerating Kerr-NUT black hole. It has well defined limits to all the type-D black holes of general relativity, including the elusive (type-D) accelerating Taub-NUT spacetime. Extension to the presence of the cosmological constant is also provided.