Exotic Behaviors of Space-time in Einstein-Maxwell Theory

TL;DR

This paper explores how extended charge distributions in Einstein-Maxwell theory create unique space-time structures with regions resembling positive and negative mass densities, affecting geodesic trajectories and space-time volume.

Contribution

It reveals novel space-time features induced by static, spherically symmetric charges and analyzes their effects on geodesics and volume forms in Einstein-Maxwell theory.

Findings

Electric fields source space-time features similar to positive and negative mass densities.

Conditions for these behaviors are detailed.

Impacts on geodesic trajectories and volume forms are analyzed.

Abstract

This paper examines the structure of electric fields and space-times created by extended finite distributions of irrotational static and spherically-symmetric charge. The resulting electric fields are found to source features in space-time commonly associated with the presence of fields with locally positive and negative mass densities, with the sign of the mass corresponding to the sign of the electric field gradient. The conditions detailing these behaviors are discussed. The effects of these structures on trajectories of time-like geodesics and the volume form are also presented.