Finding components of Riemann curvature tensor on a diagonal metric
I remember my lecturer saying something about finding all the components of a Riemann curvature tensor using its properties of symmetry but I can't remember the specifics. So I was hoping that someone here would be able to help me. I know this is to do with General Relativity, but I was told that GR is based on DG so I'm hoping this is the correct place to ask the question.
I would like to know if there is a simpler method to finding all of the components of the Riemann curvature tensor without going and calculating all the different combinations that are possible, which would take too long in a test or exam situation. We usually work with diagonal metrics, so besides making the connection coefficients easier to find, would this have any other advantages. If there is a simpler method it would make my life a whole lot easier.