Flux-balance laws in scalar self-force theory

Understand

The motion of a radiating point particle can be represented by a series of geodesics whose "constants" of motion evolve slowly with time.

• The evolution of these constants of motion can be determined directly from the self-force equations of motion.
• In the presence of spacetime symmetries, the situation simplifies: there exist not only constants of motion conjugate to these symmetries, but also conserved currents whose fluxes can be used to determine their evolution.
• Such a relationship between point-particle motion and fluxes of conserved currents is a flux-balance law.