Electrostatics in wormhole spacetimes

Abstract

Regarding the static form of Maxwell’s equations in wormhole background geometry, we obtain a generalised form of Laplace’s equation. Because of peculiar geometry of the throat, lines of force that enter the wormhole at one mouth and emerge from the other, initially converge and then diverge. So, for a remote observer the wormhole can act as a charge distribution that modifies the potential, mainly around the throat. Here, the exact solutions for the potential are obtained and by considering an equivalent dielectric media and finding polarisation charge distributions the effect of the wormhole geometry on the potential is justified. It is assumed that real sources of the potential are distributed far from the throat and do not contribute to the stress-energy tensor of the wormhole.

Keywords

• traversable wormhole
• Maxwell’s equations
• boundary conditions
• dielectric media