Emission of gravitational radiation from ultrarelativistic sources

Recent observations suggest that blobs of matter are ejected with ultrarelativistic speeds in various astrophysical phenomena such as supernova explosions, quasars, and microquasars. In this paper we analyze the gravitational radiation emitted when such an ultrarelativistic blob is ejected from a massive object. We express the gravitational wave by the metric perturbation in the transverse-traceless gauge, and calculate its amplitude and angular dependence. We find that in the ultrarelativistic limit the gravitational wave has a wide angular distribution, like 1+cosθ. The typical burst's frequency is Doppler shifted, with the blueshift factor being strongly beamed in the forward direction. As a consequence, the energy flux carried by the gravitational radiation is beamed. In the second part of the paper we estimate the anticipated detection rate of such bursts by a gravitational-wave detector, for blobs ejected in supernova explosions. Dar and De Rujula recently proposed that ultrarelativistic blobs ejected from the central core in supernova explosions constitute the source of gamma-ray bursts. Substituting the most likely values of the parameters as suggested by their model, we obtain an estimated detection rate of about 1 per year by the advanced LIGO-II detector.