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Question: all things about tensor

Question:all things about tensor

Dark Energy 100 Maple 2018
July 23 2018
1

Hello my friends

I have some problems with maple 18. I try to consider and extract some things about tensor such as contraction.

for instance, suppose we have metric=-exp(alpha(r))*(dt^2)+exp(beta(r))*(dr^2)+r^2*(dtheta^2)+r^2*(sin(theta)^2)*(dphi^2). how we can find all Riemann tensor and corresponding contraction, Ricci tensor and its contraction and even Weyl tensor and its contraction. unfortunately, I attempt to find them by using some other examples on the net but they don't help me to calculate them when time is the first element in coordinate, not last ( t,r,theta,phi) not (r,theta,phi)

thanks with the best regard
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