On the Static Spacetime of a Single Point Charge

TL;DR

This paper identifies a subclass of electromagnetic theories leading to static, spherically symmetric spacetimes with minimal singularities and finite energy, analyzing their properties and geodesic behavior.

Contribution

It characterizes a unique class of Lagrangian-based electromagnetic theories with minimal singularities and finite energy in static, spherically symmetric spacetimes, including their geometric and physical properties.

Findings

Spacetimes have conical singularity at the center.

Total energy equals the ADM mass.

For low mass-to-charge ratio, no horizons or trapped geodesics.

Abstract

Among all electromagnetic theories which (a) are derivable from a Lagrangian, (b) satisfy the dominant energy condition, and (c) in the weak field limit coincide with classical linear electromagnetics, we identify a certain subclass with the property that the corresponding static, spherically symmetric, asymptotically flat electrovacuum spacetime metric has the mildest possible singularity at its center, namely, a conical singularity on the time axis. The electric field moreover has a point defect on the time axis, its total energy is finite, and is equal to the ADM mass of the spacetime. By an appropriate scaling of the Lagrangian, one can arrange the total mass and total charge of these spacetimes to have any chosen values. For small enough mass-to-charge ratio, these spacetimes have no horizons and no trapped null geodesics. We prove the uniqueness of these solutions in the spherically symmetric class. We conclude by performing a qualitative study of the geodesics and test-charge trajectories of these spacetimes.