Removal of conical singularities from rotating C-metrics and dual CFT entropy

We show how to remove from the rotating C-metric spacetime, which describes accelerating Kerr black holes, both conical singularities. This can be done by embedding the metric into a swirling gravitational universe, through a proper Ehlers transformation. The spin-spin interaction between the external rotational background and the black hole provides the source of the acceleration without the need of rods or strings. The physical properties and entropy of the new solution are studied using near horizon and dual conformal techniques of the Kerr/CFT correspondence. The charged case is also analysed: Accelerating Reissner-Nordstrom and Accelerating Kerr-Newman space-times embedded in a swirling universe are also generated.