Self-action of a point charge in a wormhole space-time

Abstract

We consider the self-energy and the self-force for an electrically charged particle at rest in the wormhole space-time. We develop a general approach to finding the self-force and apply it to the two specific profiles of the wormhole throat with singular and with smooth curvature. The self-force for these two profiles is found in manifest form; it turns out to be an attractive force. We also find an expression for the self-force in the case of arbitrary symmetric throat profile. Far from the throat the self-force is always attractive.

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].…”

“…We consider a charged particle at rest in this spacetime, assuming that the electromagnetic field F µν is sufficiently weak so that its gravitational effect is negligible. In this case, the electromagnetic field satisfies the Maxwell equations in the background metric (1). The charge density ρ of a point charge e located at l = l 0 , ϑ = ϑ 0 and ϕ = ϕ 0 is given by ρ(l, ϑ, ϕ) = e √ −g δ(l − l 0 )δ(ϑ − ϑ 0 )δ(ϕ − ϕ 0 )…”

“…where g is the determinant of metric (1). The electrostatic potential V , defined from the electric field F 0i by F 0i = −∂ i V , obeys the electrostatic equation…”

“…as l → ±∞, because only the electric field has a direct physical meaning. A solution to equation (3) was given for the first time in the form of series of multipoles by Khusnutdinov and Bakhmatov [1]. Recently, Beskin et al [5] took up the issue of the multipole expansion.…”

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

“…Spherically symmetric wormholes were considered in Refs. [12][13][14][15]. In a previous work we studied the case of a charge in the Schwarzschild wormhole.…”