Hi guys. I am new to the Maple environment.

Was trying to do some GR calculations when the following problem arose.

restart; with(Physics);

Setup(coordinates = (X = [t, r, theta, phi]), metric = -A(r)^2*(dt^2)+B(r)^2*(dr^2)+r^2*(dtheta^2)+r^2*(sin(theta)^2)*(dphi^2));

Setup(math = true);

g_[line_element]; g_[];

Christoffel[nonzero]; Christoffel[`~mu`, alpha, beta, nonzero];

D_[mu](g_[`~alpha`, `~beta`]);

expand(D_[2](g_[`~2`, `~beta`]));

D_[2](g_[`~2`, `~2`]);

The output for the last 3 lines are:

1. 0

2. Expansion in terms of Christoffel symbols (which does equal zero on substituting various values)

3. Non-zero value.

Obviously the answer must be zero for all cases (covariant derivative of metric). So what have I missed/misunderstood here?

Regards

BuddT