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

TL;DR

This paper derives classical mechanics and radiation reaction effects from perturbations of type II Einstein-Maxwell fields, linking gravitational and electromagnetic radiation to Newton's second law.

Contribution

It shows how classical radiation reaction and momentum conservation emerge from perturbations in type II Einstein-Maxwell spacetimes, connecting general relativity to classical physics.

Findings

Bondi momentum matches classical form with radiation reaction term

Bondi mass loss corresponds to electromagnetic and gravitational dipole and quadrupole radiation

Newton's second law with radiation reaction and recoil derived from spacetime perturbations

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.