I am trying to setup a general metric with the Physics package.  The metric is composed of the Minkowski metric plus the product of two null vectors. Here is the code:

retstart;

with(Physics);

Define(l[mu],eta[mu,nu]);

eta[mu,nu] := rhs(g_[]);

Setup(g[mu,nu]=eta[mu,nu]+l[mu]*l[nu]);

I get the following error:

Error, (in Physics:-Setup) wrong argument: g[mu, nu] = l[mu]*l[nu]+(Matrix(4, 4, {(1, 1) = -1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 2) = -1, (2, 3) = 0, (2, 4) = 0, (3, 3) = -1, (3, 4) = 0, (4, 4) = 1}, storage = triangular[upper], shape = [symmetric]))

My plan is to apply the rule g[~mu,~nu]*l[mu]*l[nu] = 0 and calculate the Christoffel symbols using the metric.

I am trying to use the Physics package because the DifferentialGeometry package seemed focused on Newman-Penrose.  I will not be using NP for the calculations, only a strict calculation of the Einstein field equations from the given metric.

Thank you.

I created a null tetrad, but Maple's GRQuery returns false.  Here is the code:

I just bought Maple 17 and tried to find a couple of Newman-Penrose spin coefficients.  I can do it by hand, but when I try to do the same thing using Maple I am stuck.  Maple lets me define an orthogonal tetrad, then I convert that to a null tetrad.  But how do I then fiind spin coefficients?  I know Maple has an entire list of metrics (385) already loaded, but I need to investigate different Petrov types to develop a metric.  Thanks.