Deviation equations of Synge and Schild over \((\bar L_n,g)\)-spaces (Q2716555)

This article discusses deviation equations in spaces with affine connections where the equivalence principle is satisfied. Deviation equations which are of interest in the detection of gravitational waves can be studied to distinguish gravitational theories. A general deviation equation in affine spaces is shown to reduce to the Synge-Schild equation if the Lie-derivative of the considered vector field with respect to the deviation field vanishes. This is shown to be a sufficient, but not necessary condition which implies that the Synge-Schild equation can have additional solutions.