Regularization of electromagnetic field for self-force problem in de Sitter spacetime

Abstract

The paper is concerned with the motion of a point electric charge in de Sitter spacetime. A point particle of mass m and charge q moving on a geodesic curve produces electromagnetic field that diverges at a particle’s position. The field is determined by the electromagnetic Green’s function by Higuchi and Lee (2008 Phys. Rev. D 78 084031). The self-force contains both divergent and finite terms, and the latter are responsible for the radiation reaction. Our derivation of an effective equations of motion is based on conservation laws corresponding to the group of isometry of de Sitter space. The Nöther quantities consist of particle’s individual characteristics and energy, momentum, and angular momentum carried by particle’s electromagnetic field. Following the Detweiler–Whiting concept that a charge’s motion should only be enforced by the regular component of its own field, we ignore the divergent terms in conservation laws. We assume that the divergencies are absorbed by particle’s individual characteristics within the renormalization procedure. Finite radiative terms together with kinematic particle’s characteristics constitute ten conserved quantities of closed particle plus field system. Their differential consequences yield the effective equations of motion of radiating charge in an external electromagnetic field and gravitation. Contributions to already renormalized particle’s four-momentum and its inertial mass originated from electromagnetic field and background gravity are also derived from ten balance equations.