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 \cite{Hig2008}. 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 N"{o}ther 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.