Gravitational waves from extreme-mass-ratio inspirals using general parametrized metrics

Future space-borne interferometers will be able to detect gravitational waves at ${10}^{\ensuremath{-}3}$ to ${10}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Hz}$. In this band extreme-mass-ratio inspirals (EMRIs) can be promising gravitational-wave sources. In this paper, we investigate the possibility of testing the hypothesis that the small body is moving in Kerr spacetime against the alternative that the small body is moving in a parametrized non-Kerr metric by matching gravitational waveforms. EMRI snapshots from either equatorial geodesics or inclined geodesics suffer from the ``confusion problem.'' Our results show that, within the time scale before significant (radiation-driven) orbital evolution takes place, small and moderate deviations from the Kerr spacetime [$|{\ensuremath{\delta}}_{i}|<1$ in the notation of Ni, Jiang, and Bambi J. Cosmol. Astropart. Phys. 09 (2016) 014] can be discerned only when the Kerr spin parameter is extreme. In geodesic cases, most waveforms related to a non-Kerr metric can be mimicked by the waveform templates produced from a Kerr black hole. However, when radiation reaction is taken into consideration, the signals that are originally degenerate with each other will gradually separate and finally break the confusion. Depending on the mass ratio and other parameters of the system, the time needed to break the degeneracy can vary from several hours to several months.

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