Question: Einstein Tensor Example

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):

Was this correct?

I tried uploading the worksheet to My Files, but for some reason it's not showing up, so I'm not able upload the worksheet that I was using.






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