Detecting electric charge with extreme mass ratio inspirals

. We consider extreme mass ratio inspirals during which an electrically charged compact object with mass m p and the charge to mass ratio q inspirals around a Schwarzschild black hole of mass M . Using the Teukolsky and generalized Sasaki-Nakamura formalisms for the gravitational and electromagnetic perturbations around a Schwarzschild black hole, we numerically calculate the energy flux of both gravitational and electromagnetic waves induced by a charged particle moving in circular orbits. With one year observation of these extreme mass ratio inspirals, we show that space-based gravitational wave detector such as the Laser Interferometer Space Antenna can detect the charge to mass ratio as small as q ∼ 10 − 3 .