Gravitational wave emission under general parametrized metric from extreme mass ratio inspirals

Future space-borne interferometers will be able to detect gravitational waves at $10^{-3}$ to $10^{-1}$ Hz. At this band extreme-mass-ratio inspirals (EMRIs) can be promising gravitational wave sources. In this paper, we investigate possibility of testing Kerr hypothesis against a parametrized non-Kerr metric by matching EMRI signals. However, EMRIs from either equatorial orbits or inclined orbits suffer from the "confusion problem". Our results show that, within the time scale before radiation flux plays an important role, small and moderate deviations from the Kerr spacetime($|\delta_i|<1$) can be discerned only when spin parameter is high. In most cases, the EMRI waveforms related with a non-Kerr metric can be mimicked by the waveform templates produced with a Kerr black hole.