Two problems of theory of gravitation

TL;DR

This paper examines foundational issues in gravitation theory, focusing on the relativity of space-time geometry and the non-invariance of Einstein's equations under certain transformations, which challenge the uniqueness of physical state descriptions.

Contribution

It highlights two fundamental problems in gravitation theory: the relativity of space-time geometry and the lack of invariance of Einstein's equations under geodetic transformations.

Findings

Relativity of space-time geometry depends on the reference frame.

Einstein's equations are not invariant under geodetic transformations.

Different solutions may represent the same physical state.

Abstract

This paper aims to discuss two issues that can have a significant impact on the foundations of the theory of gravitation: (1). The existence of relativity of space-time geometry with respect to the properties of used reference frame, which is a manifestation of the long-known fact of relativity of geometry of space and time with respect to properties of measuring instruments (Henri Poincare). (2). Lack of invariance of Einstein's equations with respect to the geodetic transformations preserving unchanged the equations of motion of test particles. Because of this, the physically equivalent states are described, generally speaking, by means of different solutions of these equations. In other words, there is no one-to-one correspondence between the solutions of these equations and the set of admissible physical states