Abstract
As recent work continues to demonstrate, the study of relativistic scattering processes leads to valuable insights and computational tools applicable to the relativistic bound-orbit two-body problem. This is particularly relevant in the post-Minkowskian approach to the gravitational two-body problem, where the field has only recently reached a full description of certain physical observables for scattering orbits, including radiative effects, at the third post-Minkowskian (3PM) order. As an historically instructive simpler example, we consider here the analogous problem in electromagnetism in flat spacetime. We compute the changes in linear momentum of each particle and the total radiated linear momentum, in the relativistic classical scattering of two point-charges, at sixth order in the charges (analogous to 3PM order in gravity). We accomplish this here via direct iteration of the classical equations of motion, while making comparisons where possible to results from quantum scattering amplitudes, with the aim of contributing to the elucidation of conceptual issues and scalability on both sides. We also discuss further extensions to radiative quantities of recently established relations, which analytically continue certain observables from the scattering regime to the regime of bound orbits, applicable for both the electromagnetic and gravitational cases.
Highlights
The dawn of gravitational-wave astronomy [1,2,3,4,5] and the promise of more sensitive future detectors [6,7,8] have renewed interest in varied approaches to solving the two-body problem in general relativity (GR)
This is relevant in the post-Minkowskian approach to the gravitational two-body problem, where the field has only recently reached a full description of certain physical observables for scattering orbits, including radiative effects, at the third post-Minkowskian (3PM) order
By performing the momentum-space integral given in Eq (6.32) of Ref. [33], we find that Eq (1.18) precisely matches the direct calculation of the momentum radiated to infinity by the EM field
Summary
The dawn of gravitational-wave astronomy [1,2,3,4,5] and the promise of more sensitive future detectors [6,7,8] have renewed interest in varied approaches to solving the two-body problem in general relativity (GR). A significant milestone in the gravitational case has been the recent completion of the calculation of the relativistic impulse (net change in momentum) of each body, in the scattering of two spinless massive bodies, at the third postMinkowskian (3PM) order As we will detail below, the complete (conservative plus radiative) 3PM impulses are determined by the complete 3PM scattering angle along with the total linear (energy-)momentum radiated away in gravitational waves, first appearing at 3PM order. In addition to including radiative effects, another advantage of the classical method is that it is relatively simple to automate the iteration to go to higher orders with the only potential challenge being computation of one-dimensional integrals This may be useful for efficiently computing scattering observables, which can be used for subsequently understanding bound orbits. I B summarizes our investigations of unbound-to-bound continuation
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