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 super-nova 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 + cos theta. 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 super-nova 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.