Abstract
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 , at or near the speed of light. The radiation (in the speed-of-light case) near the forward and backward directions , , where is the angle from the symmetry axis in the center-of-mass frame, is given by the series for the news function of retarded time and angle ; successive terms can in principle be found from a perturbation treatment. Here the form of is presented. Knowledge of 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 , 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 on retarded times roughly 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 and in ; this gives an efficiency of 16.4% for gravitational wave generation.
- Received 4 February 1992
DOI:https://doi.org/10.1103/PhysRevD.46.694
©1992 American Physical Society