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

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.