Can the notion of a homogeneous gravitational field be transferred from classical mechanics to the Relativistic Theory of Gravity ?

TL;DR

This paper investigates whether the classical concept of a homogeneous gravitational field can be extended to the Relativistic Theory of Gravitation, highlighting fundamental differences and unresolved issues related to causality.

Contribution

It compares the generalization of homogeneous gravitational fields in Einstein's General Relativity and RTG, identifying causality violations in RTG solutions.

Findings

RTG solutions do not satisfy the Causality Principle

Significant differences exist between GR and RTG in this context

The problem remains open in RTG for a proper generalization

Abstract

The generalization of the concept of homogeneous gravitational field from Classical Mechanics was considered in the framework of Einstein's General Relativity by Bogorodskii. In this paper, I look for such a generalization in the framework of the Relativistic Theory of Gravitation. There exist a substantial difference between the solutions in these two theories. Unfortunately, the solution obtained according to the Relativistic Theory of Gravitation can't be accepted because it doesn't fulfill the Causality Principle in this theory. So, it remains open in RTG the problem of finding a generalization of the classical concept of homogeneous gravitational field.