![]() Can anybody help?Īs mentioned in the comments calculating algebraic expressions for the Ricci tensor containing the metric, its inverse and its first and second derivatives is straight forward using computer algebra. But for my aims, I would need references, rather than do the computations, reporting formulas giving the Ricci tensor using the metric explicitly. Besides, Christoffel symbols are given through the metric and one can do some algebra to get such kind of expressions. Next, by using divergence of the tensors, the Euler equations are. This is easy to understand because it is a straightforward way to perform practical computations and the formulas one obtains are elegant and easy to grasp. Firstly, Christoffel symbols and tensors for perfect fluids on FLRW background are calculated. In textbooks about general relativity, it is common to present the Riemann and Ricci tensors using the Christoffel symbols. This is a request for references, mainly for educational aims. Answers containing only a reference to a book or paper will be removed! Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. ) is a metric based on the exact solution of the Einstein field equations of general relativity. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. The FriedmannLemaîtreRobertsonWalker metric ( FLRW / fridmn lmtr. ![]() Before answering, please see our policy on resource recommendation questions. ![]()
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