Complex Scalar Field in General Relativity

Abstract

This paper introduces complex scalar fields in general relativity to describe charged, gravitating particles with zero spin. A class of exact solutions of the combined Maxwell-Einstein-Klein-Gordon field equations is found that may represent complete models of matter. One of the models discussed is spherically symmetric and the remaining class does not assume any specific symmetry. Such exact solutions are possible only if the mass parameter equals the charge parameter in magnitude, so that physically speaking, matter is in equilibrium under the mutual action of electromagnetic and gravitational forces.