A solution of the Einstein-Maxwell equations describing conformally flat spacetime outside a charged domain wall

TL;DR

This paper presents a new exact solution to the Einstein-Maxwell equations that models the spacetime outside a charged domain wall, revealing a counterintuitive repulsive gravity effect due to wall strain.

Contribution

It introduces a conformally flat, static solution for the Einstein-Maxwell equations describing the exterior of a charged domain wall, with analysis of gravitational behavior and wall strain effects.

Findings

Gravity is repulsive outside the charged wall despite positive electric mass.

The solution is conformally flat and static, fitting the physical scenario.

Wall strain causes the repulsive gravitational effect.

Abstract

We derive and discuss the physical interpretation of a conformally flat, static solution of the Einstein-Maxwell equations. It is argued that it describes a conformally flat, static spacetime outside a charged spherically symmetric domain wall. The acceleration of gravity is directed away from the wall in spite of the positive gravitational mass of the electric field outside the wall, as given by the Tolman-Whittaker expression. The reason for the repulsive gravitation is the strain of the wall which is calculated using the Israel formalism for singular surfaces.