Relativistic Space-Times Having Corresponding Geodesics Final Report

Pairs of Relativistic Space-Times are classified according to their Segre characteristics. Suitable bases consisting of pseudo-orthonormal tetrads are constructed and the condition that the spaces should have corresponding geodesics is imposed. contain spaces with corresponding geodesics. It is found that the [3, 1] and [(3, 1)] classes contain spaces with corresponding geodesics. Of these metrics, the vacuum ones are shown to be algebraically special, in the sense of the Petrov classification.