Can the Notion of a Homogeneous Gravitational Field be Transferred from Classical Mechanics to the Relativistic Theory of Gravity?

Bogorodskii generalized the classical mechanical concept of a homogeneous gravitational field to the case of Einstein's general relativity. We seek such a generalization to the case of the relativistic theory of gravity. The corresponding solutions in these two theories differ substantially. The solution obtained in accordance with the relativistic theory of gravity does not satisfy the causality principle in that theory. The problem of constructing a generalization of the classical notion of a homogeneous gravitational field in the framework of the relativistic theory of gravity therefore remains open.