The command CongruenceProperties returns a table of properties associated to a line congruence defined by a unit (time-like or space-like) vector field  or a null vector field .

Let , set . The following scalar and tensor fields are calculated by the first calling sequence.

The left-hand side of the Raychaudhuri equation  valid when the congruence is geodesic (0), where  is the Ricci tensor and   is also calculated.

The first calling sequence returns a table with indices "Acceleration", "Expansion", "RotationTensor", "ShearTensor", "Raychaudhuri".

The remaining three calling sequences apply only to an affinely parameterized, geodesic null congruence , that is,  and

The second calling sequence requires  where Set   and

The second calling sequence returns a table with 8 indices "Expansion", "RotationNormSquared" "ShearNormSquared", "RotationTensor", "RotationScalar", "ShearTensor" , "ComplexExpansion" and "Raychaudhuri".

The third calling sequence calculates: Expansion: Θ =   Rotation norm squared = and Shear norm squared = The definitions are as in the second calling sequence but, as these scalars do not in fact depend upon the choice of L, only the vector K is needed as input. The third calling sequence returns a table with indices "Expansion", "RotationNormSquared", "ShearNormSquared" and "Raychaudhuri".

Finally, from the 4th calling sequence we set  and  and calculate, in addition to the 8 quantities calculated for the second calling sequence , Newman-Penrose Spin Coefficients.