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## Summary:

- How can one drop "dtdr" terms in RW metric

## Main Question or Discussion Point

To arrive at the Robertson-Walker metric for a spatially homogeneous and isotropic cosmology, one first writes down the the metric for spatial sections i.e. constant t surfaces,

dσ

where f(r) can take only 3 special forms, and then one promptly writes the metric for general case when cosmic time, t, is non-constant to be the RW form,

ds

My question is how can one rule out "dtdr" terms in the second step?

dσ

^{2}= d^{2}+f^{2}(r) (dθ^{2}+ sin^{2}θ dφ^{2}),where f(r) can take only 3 special forms, and then one promptly writes the metric for general case when cosmic time, t, is non-constant to be the RW form,

ds

^{2}= -dt^{2}+ a^{2}(t) dσ^{2}.My question is how can one rule out "dtdr" terms in the second step?