The relativistic uniform model: the metric of the covariant theory of gravitation inside a body

TL;DR

This paper derives the metric inside a uniform spherical body within the covariant theory of gravitation, simplifying calculations and clarifying differences from general relativity's Reissner-Nordström metric.

Contribution

It provides an exact solution for the metric inside a uniform sphere in covariant gravitation theory, highlighting differences from general relativity.

Findings

Sum of stress-energy tensors inside the body vanishes

Explicit metric components inside the body are calculated

Differences between CTG and GR metrics are analyzed

Abstract

It is shown that the sum of stress-energy tensors of the electromagnetic and gravitational fields, the acceleration field and the pressure field inside a stationary uniform spherical body within the framework of relativistic uniform model vanishes. This fact significantly simplifies solution of equation for the metric in covariant theory of gravitation (CTG). The metric tensor components are calculated inside the body, and on its surface they are combined with the components of external metric tensor. This also allows us to exactly determine one of the two unknown coefficients in the metric outside the body. Comparing the CTG metric and the Reissner-Nordstr\"om metric in general theory of relativity shows their difference, which is a consequence of difference between equations for the metric and different understanding of essence of cosmological constant.