GRAVITATIONAL-RADIATION IN BLACK-HOLE COLLISIONS AT THE SPEED OF LIGHT .3. RESULTS AND CONCLUSIONS

This paper summarizes results following from the two preceding papers, I and II, on the gravitational radiation emitted in the head-on collision of two black holes, each with energy-mu, at or near the speed of light. The radiation (in the speed-of-light case) near the forward and backward directions theta=0, pi, where theta is the angle from the symmetry axis in the center-of-mass frame, is given by the series c0(tau, theta) = 0a2n(tau/mu)sin(2n)theta for the news function co of retarded time tau and angle-theta, successive terms can in principle be found from a perturbation treatment. Here the form of a2(tau/mu) is presented. Knowledge of a2 allows the new mass-loss formula of paper I to be applied, giving a calculation of the mass of the (assumed) final Schwarzschild black hole. Since the "final mass" resulting from the calculation exceeds 2-mu, the assumptions of the new mass-loss formula must not all hold. The most likely explanation is that there is a "second burst" of radiation present in the space-time, centered for small angles-theta on retarded times roughly \8-mu-ln-theta/ later than the "first burst" described above. A more realistic crude estimate of the energy emitted in gravitational waves is given by the Bondi expression, taking only the first two terms a0 and a2 in c0; this gives an efficiency of 16.4% for gravitational wave generation.