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.