GRAVITATIONAL-WAVES BY COMPACT STARS ORBITING AROUND ROTATING SUPERMASSIVE BLACK-HOLES

To investigate the orbital evolution of compact stars moving around a supermassive black hole (SMBH) we have calculated the energy and angular momentum fluxes of gravitational waves induced by a test particle of mass orbiting on the equatorial plane of a rotating black hole of mass M with eccentric orbits. First we analytically derive the post-Newtonian (PN) formula of the energy flux, and then, to see the relativistic effects correctly, we perform numerical calculations of the perturbation around a Kerr black hole. It is found that for highly relativistic orbits, the PN formula underestimates the energy fluxes by a factor 10. We have also found that, in the case of highly relativistic and highly eccentric orbits, due to the spin (a) of the black hole, the energy flux changes by a factor of 10a/M. Hence the orbital evolution of a compact star in the vicinity of a SMBH, which will exist in galactic nuclei, is largely affected by the spin angular momentum of the SMBH as well as other relativistic effects. The detection rate of gravitational waves from a SMBH by means of the proposed laser interferometric gravitational wave detector in space, such as LISA, also depends on these relativistic effects. A possibility of extracting the parameters of the SMBH from a signal of gravitational waves is also considered. © 1994 The American Physical Society.