Gravitational effects in terms of paths in Minkowski space

TL;DR

This paper introduces a coordinate-free, model-independent method using the group of paths in Minkowski space to analyze gravitational effects, facilitating observational analysis without relying on specific space-time geometries.

Contribution

It develops a novel formalism based on path groups that allows gravitational effects to be studied without predefined geometric models or coordinates.

Findings

Enables analysis of gravitational effects without specific geometric assumptions

Provides a formalism for interpreting observational data in curved space-time

Introduces the concept of flat models for curves in Minkowski space

Abstract

An approach is developed which enables one to analyze gravitational effects without usage of any concrete model of geometry (or a class of models of geometry) of space-time and even without any coordinate system. Instead, the formalism of the group of paths is used. An element of this group (a class of curves in Minkowski space) is associated with each curve in the curved space-time and called its `flat model'. The analysis of observational data in terms of flat models of closed curves is interpreted as a formalization of the analysis which a `naive observer' (knowing nothing about the space-time being curved) applies to his observations.