Gravitational Self-force in a Radiation Gauge

Understand

In this, the first of two companion papers, we present a method for finding the gravitational self-force in a modified radiation gauge for a particle moving on a geodesic in a Schwarzschild or Kerr spacetime.

• An extension of an earlier result by Wald is used to show the spin-weight $\pm 2$ perturbed Weyl scalar ($\psi_0$ or $\psi_4$) determines the metric perturbation outside the particle up to a gauge transformation and an infinitesimal change in mass and angular momentum.
• A Hertz potential is used to construct the part of the retarded metric perturbation that involves no change in mass or angular momentum from $\psi_0$ in a radiation gauge.
• The metric perturbation is completed by adding changes in the mass and angular momentum of the background spacetime outside the radial coordinate $r_0$ of the particle in any convenient gauge.