Connections and geodesics in the spacetime tangent bundle

Abstract

Recent interest in maximal proper acceleration as a possible principle generalizing the theory of relativity can draw on the differential geometry of tangent bundles, pioneered by K. Yano, E. T. Davies, and S. Ishihara. The differential equations of geodesics of the spacetime tangent bundle are reduced and investigated in the special case of a Riemannian spacetime base manifold. Simple relations are described between the natural lift of ordinary spacetime geodesics and geodesics in the spacetime tangent bundle.