Binary dynamics from Einstein-Maxwell theory at second post-Newtonian order using effective field theory

Abstract: The detection of gravitational waves from binary black holes sources has opened the possibility to search for electric charges and "dark" charges on black holes, the latter being candidates for dark matter. This requires theoretical predictions about the effect of charges on the inspiral of binary black holes in order to place constraint on charges. The effects of these charges on the inspiral of binary black holes can be described using Einstein-Maxwell theory. They have previously been derived up to first post-Newtonian (1PN) order, and the results were recently used to place bounds on the charge-to-mass ratio on black holes. Here we use the effective field theory approach with a metric parameterization based on a temporal Kaluza-Klein decomposition with non-relativistic gravitational fields to arrive at the Lagrangian for binary motion under the influence of charges up to 2PN order.