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This paper is motivated by the introduction of a new functional setting ofGeneral Relativity (GR) based on the adoption of suitable group non-local pointtransformations (NLPT). Unlike the customary local point transformatyionusually utilized in GR, these transformations map in each other intrinsicallydifferent curved space-times. In this paper the problem is posed of determiningthe tensor transformation laws holding for the $4-$% acceleration with respectto the group of general NLPT. Basic physical implications are considered. Theseconcern in particular the identification of NLPT-acceleration effects, namelythe relationship established via general NLPT between the $4-$accelerationsexisting in different curved-space times. As a further application the tensorcharacter of the EM Faraday tensor.with respect to the NLPT-group isestablished.

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