Kinematics of relative motion of charged test particles in general relativity

This is the first of two articles containing the definition and a detailed mathematical analysis of the concept of electromagnetic deviation in pseudo-Riemannian geometry. It presents a study of both the Lorentz equations of motion and the notion of the first electromagnetic deviation together with its equations of evolution, whereas the second article will be dealing with the notion of the second electromagnetic deviation. An interrelation of properties of the initial value problems for the Lorentz and the deviation equations is investigated. The analysis makes use of a formalism that is reparametrisation covariant and invariant under gauges of deviations defined in the paper. It is shown that by specializations of gauges one can obtain particular kinds of deviation, some of which were not discussed so far. 12 refs. (author)