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MASS-ENERGY EXTRACTION AND MOMENTUM LOSS BY GRAVITATIONAL RADIATION EMISSION IN THE COLLISION OF TWO SCHWARZSCHILD BLACK HOLES

We analyze the head-on collision of two boosted Schwarzschild black holes in the realm of Robinson-Trautman (RT) spacetimes. Characteristic initial data for the problem are constructed, and evolved via RT equation which is integrated by numerical codes based on the Galerkin method. The final configuration is that of a boosted black hole with larger (Bondi) rest mass and smaller velocity parameter. The mass-energy extraction by gravitational radiation emission is evaluated through the efficiency $\Delta$ of the process. Its distribution, as a function of the rest mass of the remnant black hole, satisfies a nonextensive law with entropic index $q \simeq 1/2$, extending to the nonlinear regime a result from the linear theory. Also the final momentum of the remnant black hole is shown to have a maximum value when the ratio $\alpha$ of the mass parameters of each individual initial black holes is approximately $0.67$. By using Bondi's mass law, we evaluate the total energy emitted in gravitational waves and check the energy conservation in the process. We show that for small values of $\alpha$ the gravitational wave emission is typically bremsstrahlung at early times.

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