(Received May 9, 1981)
The gravitational field due to a particle falling towards a Schwarzschild black hole is found to involve a divergent integral if expressed in terms of the Green function for the Teukolsky equation. It is then shown that an appropriate subtraction can be determined to tame the source term such that the difficulty is circumvented. The high-frequency asymptotic behaviour is obtained for the energy spectrum of the gravitational radiation of the particle by calculating the Green function by the WKB method and by evaluating the integral of the Green function multiplied by the tamed source both by the saddle point method and by direct numerical integration, the results being in good agreement with the corresponding part of the result Davis et al. obtained by numerical method. The analytical approach proposed here should be useful in treating more complicated case of a rotating black hole of Kerr.
URL : http://ptp.ipap.jp/link?PTP/66/1612/
DOI : 10.1143/PTP.66.1612