Geodesics in a Two-Dimensional Model of Closed Spacetime

Abstract

A simplified model of closed spacetime is considered which treats it as being imbedded in a flat, enveloping space of greater dimensionality. It is shown that in the case of expansion of space with acceleration only timelike geodesics have a solution that is infinite in time. Spacelike geodesics in this model are finite in time. This circumstance, in a natural way, forbids motion of free test particles with velocities greater than the speed of light. In principle, the conclusions of this work can be generalized to the case of a space of greater dimensionality.