A new mathematical formulation of accelerated observers in general relativity. I

Abstract

Invariant methods of modern differential geometry are used to formulate exact closed form expressions for the coordinate velocity and coordinate acceleration of a geodesic particle in the tangent space of a general relativistic accelerating rotating observer. The observation of a general vector field is shown to be definable in two ways from presymmetry and covariance arguments. Our results for the parallel translation definition of observation are shown to subsume existing work in both special and general relativity on accelerated observers.