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FLRW metric

 Definition/Summary The Friedmann-Lemaitre-Robertson-Walker metric is an exact solution of the general theory of relativity, which describes and expanding, homogeneous and isotropic universe.

 Equations The line element for the metric is $$ds^2=-dt^2+\frac{dr^2}{1-kr^2}+a(t)^2\left(d\theta^2+\sin^2\theta d\phi^2\right)\,,$$ where $(r,\theta,\phi)$ are the usual radial and angular coordinates, $t$ is the time coordinate, $a(t)$ is the scale factor, and $k$ is the (spatial) curvature of the universe.

 Recent forum threads on FLRW metric

 Breakdown Physics > Astro Cosmo >> Cosmology

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 Extended explanation Again, please feel free to edit.. maybe include general derivation of FLRW metric from assuming isotropy and homogeneity?

Commentary

 andrew1915 @ 12:42 AM Dec27-10 there is a proof in the cosmology section in the book spacetime and geometry

 andrew1915 @ 12:41 AM Dec27-10 download the book spacetime and geometry in the cosmology section there is an extensive proof,

 mysearch @ 11:27 AM Dec14-08 Does anybody have a link to a derivation of this metric? In particular, I am interested where the 1-kr^2 terms comes from. Thanks

 tiny-tim @ 03:01 AM Sep19-08 Changed title to "FLRW metric", so that it gets plenty of autolinking.