Theory of Nonlocal Point Transformations in General Relativity

Theory of Nonlocal Point Transformations in General Relativity

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A discussion of the functional setting customarily adopted in General kt-swled45ps-4a-8csa-vdim-p 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 armada tantrum skis 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.