After a long hiatus I have come back to the issue of null tetrads in the physics package in light of the updates to Maple in 2021. I have uploaded a document file to illustrate. See below. My first question concerns the labelling of elements of a null tetrad. After calling the metric 27,37 from Stephani et al, and using Setup to specify a null tetrad, Maple's choice is such that the elements labelled m and bar m are not complex. Rather, both these elements are in fact real, while the elements lablled l and n are complex, with one being the negative complex conjugate of the other. While these are just labels, they don't agree with the usual conventions for the Newman-Penrose formalism, which is disorienting. What convention is Maple using to label the elments of a null tetrad?
Next, I try to specify the null tetrad used by Stephani et al., first by converting it into covariant form (which I did by hand rather than in Maple). In Maple's default null tetrad, the order in which Maple listed the elements of the null tetrad is n, m, bar m, l (as rows in the matrix display for e_[ ]), so I followed that convention (in the conventions of Stephani et al., the first and fourh element should have scalar product -1, the second and third scalar product 1, and all other scalar products zero, which is the case). After entering the matrix and using Setup to specify the null tetrad by the matrix, I get an error message saying that the components of the metric with respect to my tetrad are not just 0, 1, and -1. Yet, executing eta_[ ] does not confirm this warning; nor does a computation by hand.
Finally, IsTetrad asserts the tetrad is not null, contrary to the fact that it is a null tetrad.
Since I have followed the conventions implicit in Maple's default null tetrad for this metric, I am puzzled as to what has gone wrong.SKMHH27_37_2021_New.mw
On the other hand, taking into account how Maple 2019 orders the coordinates in Stephani et al 27.37 and labels the null vectors in a null ttetrad, if I translate accordingly what I have in the 2021 Maple file, Maple 2019 confirms Stephani et al.'s null tetrad is indeed a null tetrad, as one would expect. See the following file.SKMHH27_37_2019_Var.mw.