tag:blogger.com,1999:blog-4005750306801645234.post6079858768126184435..comments2024-02-02T20:17:24.676+01:00Comments on Spacetime and Geometry: Exercise 8.1 N+n+1-dimensional spacetimeUnknownnoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-4005750306801645234.post-60259255738445677232023-04-06T13:55:57.301+02:002023-04-06T13:55:57.301+02:00There are quite a few errors in the subsequent cal...There are quite a few errors in the subsequent calculation. For example, all (a-dot/a)^2 terms should cancel out in (27), and the sign of ρ is wrong in (36). A quick sanity check after each calculation is to compare your result with the calculations leading to the standard Friedmann equation. When you remove all those terms containing b and set N=3, you should get the same results (other that minor differences caused by the difference between cartesian x,y,z and polar ρ,θ,φ).Petra Axolotlhttps://www.blogger.com/profile/06597951512037995047noreply@blogger.comtag:blogger.com,1999:blog-4005750306801645234.post-44957506651174347542023-04-06T13:12:42.367+02:002023-04-06T13:12:42.367+02:00Your "handwaving" derivation to get (10)...Your "handwaving" derivation to get (10) is in fact not handwaving at all. It is quite easy to prove in linear algebra that the inverse of a block-diagonal matrix diag(A, B, C) is simply diag(A^{-1}, B^{-1}, C^{-1}).Petra Axolotlhttps://www.blogger.com/profile/06597951512037995047noreply@blogger.com