  In the frame of the Kerr-Schild approach, we obtain a generalization of the
Kerr solution to a nonstationary case corresponding to a rotating source moving
with arbitrary acceleration. Similar to the Kerr solution, the solutions
obtained have the geodesic and shear free principal null congruence. The
current parameters of the solutions are determined by a complex retarded-time
construction via a given complex worldline of source. The real part of the
complex worldline defines the values of the boost and acceleration while the
imaginary part controls the rotation. The acceleration of the source is
accompanied by a lightlike radiation along the principal null congruence. The
solutions obtained generalize to the rotating case the known Kinnersley class
of the "photon rocket" solutions.
