  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.
