Electromagnetic Fields in Compact Binaries: Post-Newtonian Wave Generation and Application to Double White Dwarfs Systems

The aim of this work is twofold: (i) to properly define a wave-generationformalism for compact-supported sources embedded in Einstein-Maxwell theory,relying on matched post-Newtonian and multipolar-post-Minkowskian expansions;(ii) to apply this formalism (which is valid for any type of post-Newtoniansources) to the case of two stars with constant and aligned magnetic dipoles,by computing the fluxes of energy and angular momentum to the next-to-leadingorder, as well as the gravitational amplitude modes. Assuming eccentric orbits,we derive the evolution of orbital parameters, as well as the observables ofthe system, notably the gravitational phase for quasi-circular orbits. Finally,we give some numerical estimates for the contribution of the magnetic dipolesfor some realistic systems.