Self-force driven motion in curved spacetimes

TL;DR

This paper derives a covariant first-order correction to geodesic motion in curved spacetime, incorporating self-force effects for the extreme mass ratio two-body problem, advancing understanding of self-force driven dynamics.

Contribution

It introduces a covariant derivation of the first-order self-force correction to geodesic motion using the Dirac-Detweiler-Whiting effective field in curved spacetime.

Findings

Derived the first-order perturbative correction to geodesic motion.

Included self-force contributions and background metric effects.

Provided a covariant formulation for self-force driven motion.

Abstract

We adopt the Dirac-Detweiler-Whiting radiative and regular effective field in curved spacetime. Thereby, we derive straightforwardly the first order perturbative correction to the geodesic of the background in a covariant form, for the extreme mass ratio two-body problem. The correction contains the self-force contribution and a background metric dependent term.