Reissner-Nordstr\"om perturbation framework with gravitational wave applications

Abstract

We present a new convenient framework for modeling Reissner-Nordstr\"om black hole perturbations from charged distributions of matter. Using this framework, we quantify how gravitational wave observations of compact binary systems would be affected if one or both components were charged. Our approach streamlines the (linearized) Einstein-Maxwell equations through convenient master functions that we designed to ameliorate certain disadvantages of prior strategies. By solving our improved master equations with a point source, we are able to quantify the rate of orbital energy dissipation via electromagnetic and gravitational radiation. Through adiabatic and quasicircular approximations, we apply our dissipative calculations to determine trajectories for intermediate and extreme mass-ratio inspirals. By comparing trajectories and waveforms with varied charges to those with neutral components, we explore the potential effect of electric charge on gravitational wave signals. We observe that the case of opposite charge-to-mass ratios has the most dramatic impact. Our findings are largely interpreted through the lens of the upcoming LISA mission.