Probing deviations to Kerr geometry with extreme mass-ratio inspirals

One of the primary research aims of the Laser Interferometer Space Antenna (LISA) mission is to comprehensively map the Kerr spacetime, a fundamental pursuit in the realm of general relativity. To achieve this goal, it is essential to develop precise tools capable of discerning any deviations from the Kerr geometry. Extreme mass-ratio inspirals (EMRIs) stand out as particularly promising sources for probing the spacetime metric, offering profound insights into gravitational phenomena. In this direction, we analyze a deformed Kerr geometry, being the central source of an EMRI system, with an inspiralling object that exhibits eccentric equatorial motion. We conduct a leading-order post-Newtonian analysis and examine the deviations in gravitational wave flux and phase with their leading-order contributions. Our findings evaluate the detectability of these deviations through gravitational wave dephasing and mismatch, highlighting the pivotal role of LISA observations in advancing our understanding of spacetime geometry.