Example 1.

Define a manifold S with coordinates [t, x, y, z].

Define a metric g.

Define a null tetrad NTetrad for the metric g.  Use GRQuery to verify that NTetrad is a null tetrad.

Calculate the NP directional derivative operators defined by the null tetrad NTetrad.  The result is a table with 4 indices.

The individual directional derivatives operators can be extracted from the table NPDirDer.

Note that this coincides with the Lie derivative of f(t, x, y, z) with respect to the first vector in NTetrad.

Example 2.

With the keyword argument output = "sequence", the command NPDirectionalDerivatives will return the directional derivatives operators as a sequence. (Note that the name D is protected by Maple.)

Example 3.

When working with the NP formalism, it is usually advantageous to work with the anholonomic frame defined by the null tetrad.  To create anholonomic frames in DifferentialGeometry, see FrameData.

We can now calculate the directional derivatives operators for the null tetrad with the second calling sequence.

DifferentialGeometry, Tensor, LieDerivative, GRQuery, NullTetrad