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

The detection of gravitational waves from binary black hole 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 effects of these charges on the inspiral of binary black holes in order to place constraints on them. The effects of these charges on the inspiral can be described using Einstein-Maxwell theory. These effects have previously been derived up to the first post-Newtonian (1PN) order, and the results were recently used to place bounds on the charge-to-mass ratio of black holes. In this work, we employ the effective field theory approach, with a metric parametrization based on a temporal Kaluza-Klein decomposition and nonrelativistic gravitational fields, to derive the Lagrangian for binary motion under the influence of charges up to 2PN order. Our results provide the foundation for deriving precision predictions of the effect of charges on the inspiral of binary black holes for gravitational wave astronomy.