Accelerating and rotating black holes

An exact solution of Einstein’s equations which represents a pair of accelerating and rotating black holes (a generalised form of the spinning C-metric) is presented. The starting point is a form of the Plebański–Demiański metric which, in addition to the usual parameters, explicitly includes parameters which describe the acceleration and angular velocity of the sources. This is transformed to a form which explicitly contains the known special cases for either rotating or accelerating black holes. Electromagnetic charges and a NUT parameter are included, the relation between the NUT parameter l and the Plebański–Demiański parameter n is given, and the physical meaning of all parameters is clarified. The possibility of finding an accelerating NUT solution is also discussed.