A global isometry approach to accelerating observers in flat space–time

Abstract

A global two-point diffeomorphic extension of Lorentz transformations is constructed which preserves the global Lorentzian metric structure of flat R4. This global mapping induces, as a tangent-space mapping, instantaneous Lorentz transformations parametrized by interframe velocity functions. The elimination of pseudoterms from particle and electromagnetic field equations leads to an exact analytic expression for the affine connection needed for covariant differentiation. Examination of invariant particle equations gives an obvious proof of the equivalence principle in terms of the symmetric part of the acceleration-group connection. Transformation properties of the connection coefficients are shown to be in accord with general covariance requirements. The specific case of the rotating observer is treated exactly where it is seen that the affine connection merely supplies the exact Thomas precession term. Recent work by DeFacio et al. is found to be especially convenient for comparison with the present work. The results of the two approaches agree precisely. A summary of results indicates that the global isometry approach gives results consistent with those obtained via presymmetry arguments.