  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.
