On the principles of description of time and space relationships in frames of general relativity

TL;DR

This paper develops a framework for describing space and time relationships in curved space-time using the concepts of columns and weak columns, proposing new equations and solutions for non-inertial frames in general relativity.

Contribution

It introduces the notions of columns and weak columns for consistent measurement descriptions and derives equations for non-inertial frames in curved space-time.

Findings

Derived equations for columns and weak columns in curved space-time

Proposed criteria for inertial and non-inertial frames

Applied solutions to calculate gravitational and inertial forces

Abstract

The problem of the referring of space and time relationships between physical objects in a curved space-time is discussed. The basic notions of column and weak column that could constitute the basis for consistent general relativistic description of measurements of space and time relations are introduced and the corresponding equations are derived. A column of observers is proposed to realize still vague notion of `non-inertial frame of reference' in case of curved space-time, the criterion distinguishing `inertial columns' is suggested as well. A number of solutions of column equations is described. They are applied for calculation of gravitational, inertial (or gravitational-inertial in more general situation) and ``external" forces and the strength of gravitational field in several cases of physical interest. In particular, the `general relativistic' version of Newton's law of inverse squares is derived in case of the interaction of test particle with a static central symmetric body.