A boosted Kerr black hole solution and the structure of a general astrophysical black hole

A solution of Einstein's vacuum field equations that describes a boosted Kerr black hole relative to an asymptotic Lorentz frame at the future null infinity is derived. The solution has three parameters (mass, rotation and boost) and corresponds to the most general configuration that an astrophysical black hole must have; it reduces to the Kerr solution when the boost parameter is zero. In this solution the ergosphere is north-south asymmetric, with dominant lobes in the direction opposite to the boost. However the event horizon, the Cauchy horizon and the ring singularity, which are the core of the black hole structure, do not alter, being independent of the boost parameter. Possible consequences for astrophysical processes connected with Penrose processes in the asymmetric ergosphere are discussed.