Inertial effects of an accelerating black hole

We consider the static vacuum C metric that represents the gravitational field of a black hole of mass $m$ undergoing uniform translational acceleration $A$ such that $mA<1\mathrm{/}(3\sqrt{3})$. The influence of the inertial acceleration on the exterior perturbations of this background are investigated. In particular, we find no evidence for a direct spin-acceleration coupling.