Theory of non-local point transformations - Part 3: Theory of NLPT-acceleration and the physical origin of acceleration effects in curved space-times

TL;DR

This paper develops a new framework in General Relativity using non-local point transformations to relate accelerations and electromagnetic tensors across different curved space-times, offering novel insights into acceleration effects.

Contribution

It introduces a group of non-local point transformations in GR and derives tensor laws for acceleration and electromagnetic fields within this framework.

Findings

Established tensor transformation laws for 4-acceleration under NLPT.

Linked 4-accelerations in different curved space-times via NLPT.

Proved the tensor character of the electromagnetic Faraday tensor under NLPT.

Abstract

This paper is motivated by the introduction of a new functional setting of General Relativity (GR) based on the adoption of suitable group non-local point transformations (NLPT). Unlike the customary local point transformatyion usually utilized in GR, these transformations map in each other intrinsically different curved space-times. In this paper the problem is posed of determining the tensor transformation laws holding for the $4-$% acceleration with respect to the group of general NLPT. Basic physical implications are considered. These concern in particular the identification of NLPT-acceleration effects, namely the relationship established via general NLPT between the $4-$accelerations existing in different curved-space times. As a further application the tensor character of the EM Faraday tensor.with respect to the NLPT-group is established.