Aspects of electrostatics in a weak gravitational field

TL;DR

This paper explores electrostatics in a weak gravitational field using the Rindler metric, providing simpler derivations of known results, interpreting electrostatic potential and forces, and connecting electrostatics to radiation phenomena.

Contribution

It offers new, transparent derivations of electrostatic features in a gravitational field and interprets electrostatic energy as a source of radiation and weight.

Findings

Electrostatic potential expressed via affine parameter distance.

Electrostatic forces analyzed and interpreted in Rindler frame.

Electrostatic energy contributes to radiation and weight in a gravitational field.

Abstract

Several features of electrostatics of point charged particles in a weak, homogeneous, gravitational field are discussed using the Rindler metric to model the gravitational field. Some previously known results are obtained by simpler and more transparent procedures and are interpreted in an intuitive manner. Specifically: (i) We show that the electrostatic potential of a charge at rest in the Rindler frame is expressible as A_0=(q/l) where l is the affine parameter distance along the null geodesic from the charge to the field point. (ii) We obtain the sum of the electrostatic forces exerted by one charge on another in the Rindler frame and discuss its interpretation. (iii) We show how a purely electrostatic term in the Rindler frame appears as a radiation term in the inertial frame. (In part, this arises because charges at rest in a weak gravitational field possess additional weight due to their electrostatic energy. This weight is proportional to the acceleration and falls inversely with distance -- which are the usual characteristics of a radiation field.) (iv) We also interpret the origin of the radiation reaction term by extending our approach to include a slowly varying acceleration. Many of these results might have possible extensions for the case of electrostatics in an arbitrary static geometry. [Abridged Abstract]