Detecting electric charge with extreme mass ratio inspirals

Abstract

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 a space-based gravitational wave detector such as the Laser Interferometer Space Antenna can detect the charge to mass ratio as small as $q\ensuremath{\sim}{10}^{\ensuremath{-}3}$.