Question:General Relativity Calculation

Question:General Relativity Calculation

Maple

Can anyone help with a purely Maple solution to this problem? (i.e. not having to download anything extra.)

Just for reference I'm woking on problem number 26 in "Schaum's Outline Series " for tensor Calculus.

It gives you a Schwarzchild metric and asks you to calculate the Einstein Tensor.  I'm using the example of doing this that's given in the "tensor" package help pages.  However I'm not getting quite the right answer.

In the metric given in the problem the [1,1] component is an exponential exp(phi) and the last component is also an exponential, -exp(psi).

However the variables phi, and psi are also functions of the coordinates x1, and x4 also.  I believe it's accounting for this fact properly that's causing the discrepancies.

The way that I tried to account for this after a couple of the preliminary steps used in the "tensor" package example,  was to use the commands,

phi :=   (x1,x4) -> phi(x1,x4): , and psi := (x1,x4) -> psi(x1,x4):