Theory of non-local point transformations - Part 1: Representation of Teleparallel Gravity

TL;DR

This paper introduces non-local point transformations (NLPT) to extend the framework of General Relativity, enabling phase-space transformations that connect flat Minkowski space-time with arbitrary curved space-times, thereby addressing Einstein's Teleparallel problem.

Contribution

It develops a new class of transformations called special NLPTs that generalize reference frames in GR and solve the Teleparallel problem through phase-space mappings.

Findings

Defined and analyzed the properties of special NLPTs.

Established a method to connect Minkowski and curved space-times.

Provided a functional framework for non-local transformations in GR.

Abstract

In this paper the extension of the functional setting customarily adopted in General Relativity (GR) is considered. For this purpose, an explicit solution of the so-called Einstein's\ Teleparallel problem is sought. This is achieved by a suitable extension of the traditional concept of GR reference frame and is based on the notion of non-local point transformation (NLPT). In particular, it is shown that a solution to the said problem can be reached by introducing a suitable subset of transformations denoted here as \textit{special} \textit{NLPT}. These are found to realize a phase-space transformation connecting\emph{\}the flat Minkowski space-time with, in principle, an arbitrary curved space-time. The functional setting and basic properties of the new transformations are investigated.