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

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} ].