In a series of papers Amati, Ciafaloni and Veneziano and 't Hooft conj
ectured that black holes occur in the collision of two light particles
at Planckian energies. In this paper we discuss a possible scenario f
or such a process by using the Chandrasekhar-Ferrari-Xanthopoulos dual
ity between the Kerr black hole solution and colliding plane gravitati
onal waves, We clarify issues arising in the definition of transition
amplitude from a quantum state containing only usual matter without bl
ack holes to a state containing black holes. Collision of two plane gr
avitational waves producing a space-time region that is locally isomet
ric to an interior of black hole solution is considered. The phase of
the transition amplitude from plane waves to white and black holes is
calculated by using the Fabbrichesi, Pettorino, Veneziano and Vilkovis
ky approach, An alternative extension beyond the horizon in which the
space-time again splits into two separating gravitational waves is als
o discussed. Such a process is interpreted as the scattering of plane
gravitational waves through the creation of virtual black and white ho
les.