Self-force of a rigid ideal fluid, and a charged sphere in hyperbolic motion

TL;DR

This paper investigates the self-force on accelerating bodies, showing that a rigid ideal fluid exerts no net boundary force and deriving the electromagnetic self-force for a uniformly accelerating charged sphere.

Contribution

It introduces a new approach to calculating self-force using simultaneity planes and provides an explicit formula for electromagnetic self-force on an accelerating charged sphere.

Findings

Ideal fluid exerts no net boundary force under the new definition.

Derived an explicit series formula for electromagnetic self-force on a charged sphere.

The results clarify self-force behavior in relativistic acceleration scenarios.

Abstract

We present two results in the treatment of self-force of accelerating bodies. If the total force on an extended rigid object is calculated from the change of momentum summed over planes of simultaneity of successive rest frames, then we show that an ideal fluid, moving rigidly, exerts no net force on its boundary. Under this same definition of total force, we find the electromagnetic self-force for a spherical charged shell of proper radius R accelerating with constant proper acceleration g is (2 e^2 g/R)[ 1/12 - \sum_{n=0}^\infinity (g R)^{2n} ((2n-3)(2n-1)(2n+1)^2)^{-1} ].