Angular Momentum in Gravitational and Electromagnetic Scattering

Abstract

Conservation laws are of fundamental importance in physics. In special relativity, the well known conserved quantity of angular momentum is paired with a lesser known conserved quantity we call ``mass moment", which reduces to center of mass in the Newtonian limit. In general relativity, there are severe difficulties even defining angular momentum and mass moment, especially in the context of radiation. The goal of this thesis is to better understand the nature of these conserved quantities in relativistic physics. To gain insight, we will study the specific problem of weak-field, two-body, perturbative scattering for both gravity and electromagnetism. This problem is simple enough to be analytically tractable but complex enough to feature the radiation of angular momentum and mass moment. Previous calculations show that angular momentum is radiated at a perturbative order before energy and momentum. We calculate the full trajectories and find that the change in mechanical angular momentum of the two-particle system exactly balances the radiated angular momentum. We also calculate the shift in mass moment (a ``scoot") for the first time. However, we find a naive mismatch between the mechanical and radiated mass moment, which is reconciled by ensuring consistent choices of time slicing and asymptotic reference frame. There results establish a firm foundation for understanding angular momentum transfer in relativistic scattering.