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

## TL;DR

This study explores the potential to test the Kerr hypothesis using gravitational wave signals from EMRIs with parametrized non-Kerr metrics, highlighting challenges like the confusion problem and the influence of black hole spin.

## Contribution

It introduces a method to distinguish Kerr and non-Kerr spacetimes using EMRI signals, considering the effects of deviations and spin within a specific observational timeframe.

## Key findings

- Small deviations from Kerr can be detected at high spins.
- EMRI waveforms with non-Kerr metrics can often be mimicked by Kerr waveforms.
- Detection is limited by the confusion problem and the timescale before radiation flux impacts signals.

## Abstract

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.