Weyl-type Fields with Geodesic Lines of Force

TL;DR

This paper investigates static electrogravitational fields with Weyl-type potentials, identifying specific solutions with shearfree and shearing geodesic lines of force, including classical charged configurations and a new algebraically general solution.

Contribution

It derives all shearfree geodesic line solutions for Weyl-type electrogravitational fields and introduces a new shearing solution outside the Majumdar-Papapetrou class.

Findings

Fields of a charged sphere, rod, and plate identified

New shearing geodesic solution found with flat equipotential surfaces

Solution can have mass greater or less than charge magnitude, but not in the Majumdar-Papapetrou class

Abstract

The static electrogravitational equations are studied and it is shown that an aligned type D metric which has a Weyl-type relationship between the gravitational and electric potential has shearfree geodesic lines of force. All such fields are then found and turn out to be the fields of a charged sphere, charged infinite rod and charged infinite plate. A further solution is also found with shearing geodesic lines of force. This new solution can have $m>|e|$ or $m<|e|$, but cannot be in the Majumdar-Papapetrou class (in which $m = |e|$). It is algebraically general and has flat equipotential surfaces.