Gravitational waves by compact star orbiting around rotating supermassive black holes

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Abstract
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 μ orbiting on the equatorial plane of a rotating black hole of mass M≫μ 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.