Theory of Nonlocal Point Transformations in General Relativity

Abstract

A discussion of the functional setting customarily adopted in General Relativity (GR) is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs). While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern(1)a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory;(2)the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times;(3)the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and(4)the diagonalization of nondiagonal metric tensors.