  We examine the efficiency of gravitational bremsstrahlung production in the
process of head-on collision of two boosted Schwarzschild black holes. We
constructed initial data for the characteristic initial value problem in
Robinson-Trautman spacetimes, that represent two instantaneously stationary
Schwarzschild black holes in motion towards each other with the same velocity.
The Robinson-Trautman equation was integrated for these initial data using a
numerical code based on the Galerkin method. The final resulting configuration
is a boosted black hole with Bondi mass greater than the sum of the individual
mass of each initial black hole. Two relevant aspects of the process are
presented. The first relates the efficiency $\Delta$ of the energy extraction
by gravitational wave emission to the mass of the final black hole. This
relation is fitted by a distribution function of non-extensive thermostatistics
with entropic parameter $q \simeq 1/2$; the result extends and validates
analysis based on the linearized theory of gravitational wave emission. The
second is a typical bremsstrahlung angular pattern in the early period of
emission at the wave zone, a consequence of the deceleration of the black holes
as they coalesce; this pattern evolves to a quadrupole form for later times.

General Relativity and Quantum Cosmology