Testing Gravity Theory With Extreme Mass-Ratio Inspirals: Recent Progress ^†

A compact object captured by a supermassive black hole, named as extreme-mass-ratio inspiral (EMRI), is one of the most important gravitational wave sources for low-frequency interferometers such as LISA, Taiji, and TianQin. EMRIs can be used to accurately map the space-time of the central massive body. In the present paper, we introduce our recent progress on testing gravity theory with EMRIs. We demonstrate how to constrain gravitational wave dispersion and measure the deviation of the central body from the Kerr black hole. By using binary-EMRIs, the gravitational recoil and mass loss due to merger will be measured in a higher accuracy compared with the current LIGO observations. All these potential constrains and measurements will be useful for test of the gravity theory.