Non--Localizability of Electric Coupling and Gravitational Binding of Charged Objects

TL;DR

This paper demonstrates that in general relativity, the electric coupling energy of a charged object cannot be localized and is not gravitationally bound, ruling out the existence of purely electromagnetic mass objects.

Contribution

It provides an explicit expression showing electric coupling's non-localizability and its lack of gravitational binding in charged objects within general relativity.

Findings

Electric coupling contributes non-localizable mass

Pure electromagnetic mass objects cannot exist in general relativity

Electric coupling is not bound by gravity

Abstract

The energy--momentum tensor in general relativity contains only localized contributions to the total energy--momentum. Here, we consider a static, spherically symmetric object consisting of a charged perfect fluid. For this object, the total gravitational mass contains a non--localizable contribution of electric coupling (ordinarily associated with electromagnetic mass). We derive an explicit expression for the total mass which implies that the non--localizable contribution of electric coupling is not bound together by gravity, thus ruling out existence of the objects with pure Lorentz electromagnetic mass in general relativity.