Generalized Nonsingular Solutions for the Scalar Meson Field of a Point Charge in General Relativity Theory

TL;DR

This paper derives a unified, nonsingular solution for the gravitational and scalar meson fields of a point charge in general relativity, enabling finite calculations of nucleon properties.

Contribution

It presents a novel, nonsingular solution to the coupled gravitational and scalar meson field equations for a point charge in general relativity.

Findings

The solution is nonsingular at all points.

It generalizes the Yukawa potential.

It allows finite calculation of nucleon mass and self-energy.

Abstract

It has been shown that in investigating the electromagnetic and meson fields of elementary particles, the effects of gravitational interaction cannot be neglected. The present note is an attempt to find solutions to the equations of the general relativistic gravitational and scalar meson fields of a point nuclear charge. The solution is nonsingular at all points of the gravitational and meson fields. Although it contains several functions whose form is not given, this solution can be used to obtain the potential of the scalar meson field, which is a generalization of the Yukawa potential; furthermore, it makes it possible to calculate the mass and self-energy of the nucleon, which turn out to be finite.