The discussion centers on the derivation of the Robertson-Walker (RW) metric, specifically addressing the exclusion of "dtdr" terms in the metric formulation. The RW metric is expressed as ds^2 = -dt^2 + a^2(t) dσ^2, where dσ^2 = d^2 + f^2(r)(dθ^2 + sin^2θ dφ^2). Participants reference Carroll's lecture notes on General Relativity and emphasize the importance of spatial homogeneity and isotropy in allowing the metric to be foliated into spacelike slices. The conversation also touches on the implications of synchronous coordinates and the conditions under which metric terms can be simplified.
Cosmologists, theoretical physicists, and students of General Relativity seeking to understand the derivation and implications of the Robertson-Walker metric in cosmological models.
Roy_1981 said:Thats actually not true, you can put a dtdr term, it does not violate spatial isotropy or homogeneity. dtdφ of course does, which is why I did not put in the metric I mentioned in my original post.