Newton's 2nd Law, Radiation Reaction & Type II Einstein-Maxwell Fields

Abstract

Considering perturbations off the Reissner-Nordstrom metric while keeping the perturbations in the class of type II Einstein-Maxwell metrics, we do a spherical harmonic expansion of all the variables up to the quadrupole term. This leads to a rather surprising results. Referring to the source of the metric as a type II particle (analogous to referring to a Schwarzschild-Reissner-Nordstrom or Kerr-Newman particle), we see immediately that the Bondi momentum of the particle take the classical form of mass times velocity plus an electromagnetic radiation reaction term while the Bondi mass loss equation become the classical gravitational and electromagnetic (electric and magnetic) dipole and quadrupole radiation. The Bondi momentum loss equation turns into Newtons second law of motion containing the Abraham, Lorentz, Dirac radiation reaction force plus a momentum recoil (rocket) force while the reality condition on the Bondi mass aspect yields the conservation of angular momentum.