Self-force of a point charge in the spacetime of a massive wormhole

Abstract

We consider the self-potential and the self-force for an electrically charged particle at rest in the massive wormhole space-time. We develop general approach for the renormalization of electromagnetic field of such particle in the static space-times and apply it to the space-time of wormhole the metric of which is a solution to the Einstein-scalar field equations in the case of a phantom massless scalar field. The self-force is found in manifest form; it is an attractive force. We discuss the peculiarities due to the parameter of the wormhole mass.

Electrostatics in a simple wormhole revisited

“…The main purpose of all these works [1][2][3][4][5] is to determine the electrostatic self-force acting on the point charge within this multipole formalism. We note that the self-force for the scalar field has been also considered [6,7].…”

Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge

“…We defined the bulk term so that it corresponds to a field sourced by the test charge placed in a space-time without the shell. This field contains the divergent part of the potential to be renormalized with well-known procedures [23][24][25]. The shell field left over accounts for the discontinuity of the extrinsic curvature κ p q of the TSST and contains information of the two constituent geometries of the complete space-time.…”

“…To obtain (27) we operate analogously to (25) with r 0 = r . 1 Note that the factor ∂ r ( √ −g gtt grr ) in Eq.…”

“…1 Note that the factor ∂ r ( √ −g gtt grr ) in Eq. (20) generates a delta function due to the step-jump of the metric at r = r i but it does not appear in (25), i.e., the extra terms arising from the discontinuity of the extrinsic curvature over the shell do not introduce electric sources to the electrostatic potential.…”

“…[24] or [25] for a full derivation 2 ). The terms of 2 In (37) there is an overall sign difference with respect to the cited literature arising from the convention taken for the Maxwell equations (14).…”