On a Semi-Relativistic Treatment of the Gravitational Radiation from a Mass Thrusted into a Black Hole

•A semi·relativistic treatment estimating the gravitational radiation emitted by a particle thrusted into a Schwarzschild black hole with a finite kinetic energy at infinity is presented on the two extreme assumptions: (a) The particle moves along a geodesic in a curved space and (b) the particle radiates as if it were in flat space-time. The structure of the burst and beaming process of gravitational radiation are studied. The merit of this approach lies in its simplicity and in providing a direct and complemen tary understanding of the results obtained by a fully relativistic treatment. The recent progress in the development of a new family of gravitational wave antennae!) and the possibility of achieving the accuracy required to observe predicted levels of gravitational wave signals coming from galactic sources,2) have made a new analysis of the detailed structure of bursts of gravitational waves necessary. In this paper we propose a semi-relativistic treatment for the estimation of the gravitational radiation emitted by a particle thrusted into a Schwarzschild black hole with a finite kinetic energy at infinity. Following the approach used in Ref. 3) we have made two extreme assumptions: (a) the particle moves along a geodesic in the Schwarzschild geometry, and (b) the particle radiates as if it were in flat space-time. However, contrary to Ref. 3), in which the stress is mainly on the energy spectrum of the radiation, here we are interested in the temporal structure of the burst. Therefore, we introduce an approximation technique by which the details of the radiating process can be readily studied and easily compared with the results obtained by using a fully relativistic treat ment. The fully relativistic treatment of this same process is presented in Ref. 4). § 2. Perturbations induced by a particle thrusted into a black hole in the semi-relativistic treatment