Scalar mesostatic field with regard for gravitational effects

TL;DR

This paper discusses the exact solutions of Einstein's equations for scalar mesostatic fields, highlighting historical developments, and analyzes gravitational effects on the field's behavior near a point source, including energy divergence.

Contribution

It clarifies the historical discovery of static scalar solutions and provides an exact solution considering gravitational effects on a mesostatic scalar field.

Findings

Exact solution for massless scalar field with gravity obtained

Gravitational effects significantly alter field behavior near source

Total energy diverges logarithmically at small distances

Abstract

(Foreword by translator.) The aim of present translation is to clarify the historically important question who was the pioneer in obtaining of exact static solutions of Einstein equations minimally coupled with scalar field. Usually, people cite the works by Janis, Newman, Winicour (Phys. Rev. Lett. 20 (1968) 878) and others authors whereas it is clear that JNW rediscovered (in other coordinates) the Fisher's solution which was obtained 20 years before, in 1947. Regrettably, up to now I continue to meet many papers (even very fresh ones) whose authors evidently do not know about the Fisher's work, so I try to remove this gap by virtue of present translation and putting it into the LANL e-print archive. (Original Abstract.) It is considered the scalar mesostatic field of a point source with the regard for spacetime curvature caused by this field. For the field with $\mass = 0$ the exact solution of Einstein equations was obtained. It was demonstrated that at small distance from a source the gravitational effects are so large that they cause the significant changes in behavior of meson field. In particular, the total energy of static field diverges logarithmically.