Introduction The theory of geodesic congruences is extensively covered in many textbooks (see References); what follows in the introduction is a brief summary. Consider a 1-parameter family of timelike geodesics ##\gamma_s(\lambda)##, where ##s## labels each geodesic in the family whilst ##\lambda## is an affine parameter along each ##\gamma_s##. Then the vector field ##\xi \equiv \partial / \partial…