Deformations and momentum-energy complexes

Summary

Let ℛ be a simply connected region of an Einstein-Riemann space that is filled by the trajectories of a time-oriented normal congruence K. The most general form of the momentum-energy tensor is determined under the assumption that we know the deformation of the metric tensor under transport along K. The time-like eigenvector and associated eigenvalue of this momentum-energy tensor are examined.