Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs

Direct detection of gravitational waves and binary black hole mergers have proven to be remarkable investigations of general relativity. In order to have a definitive answer as to whether the black hole spacetime under test is the Kerr or non-Kerr, one requires accurate mapping of the metric. Since EMRIs are perfect candidates for space-based detectors, Laser Interferometer Space Antenna (LISA) observations will serve a crucial purpose in mapping the spacetime metric. In this article, we consider such a study with the Johannsen spacetime that captures the deviations from the Kerr black hole and further discuss their detection prospects. We analytically derive the leading order post-Newtonian corrections in the average loss of energy and angular momentum fluxes generated by a stellar-mass object exhibiting eccentric equatorial motion in the Johannsen background. We further obtain the orbital evolution of the inspiralling object within the adiabatic approximation and estimate the orbital phase. We lastly provide the possible detectability of deviations from the Kerr black hole by estimating gravitational wave dephasing and highlight the crucial role of LISA observations.