| Abstract : | The classical two-body problem in general relativity (GR) is notoriously complex. Hence, one resorts to different approximation schemes to get an analytic handle on the problem. With the rapid advancement in gravitational wave detectors, developing analytical methods for accurate theoretical modeling of binary gravitational systems has become increasingly crucial. One of the most utilized and well-studied analytical approximations is the post-Newtonian (PN) approximation, wherein we study the binary dynamics in the weak-field and small-velocity limits. However, in several physical scenarios, one is forced to relax the small-velocity approximation. In such cases, the post-Minkowskian (PM) approach is more appropriate, wherein observables are computed as a weak-field expansion without restriction on the velocities. To efficiently model bound binary systems using the PM results, it is advantageous to devise an effective one-body formulation of the original two-body problem. To this end, it is instructive to do this exercise on a relatively simpler system, namely, the relativistic two-body scattering in electromagnetism (EM). For the first time, we provide the EOB formalism for leading-order radiative effects in classical relativistic scattering in EM. Although the EM problem is devoid of the non-linearities of GR, it still has several difficulties encountered in the gravitational case, making it a useful toy model for understanding PM dynamics. After discussing the main results of the EM case, we outline the lessons for future extensions to the gravitational case. A concrete EOB formulation for PM gravity, which also accounts for radiative effects, will complement the well-known EOB approaches for PN dynamics and also enhance our analytical grasp on the binary dynamics in GR. |
