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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

[tex]ds^2=-dt^2+\frac{dr^2}{1-kr^2}+a(t)^2\left(d\theta^2+\sin^2\theta d\phi^2\right)\,,[/tex]

where [itex](r,\theta,\phi)[/itex] are the usual radial and angular coordinates, [itex]t[/itex] is the time coordinate, [itex]a(t)[/itex] is the scale factor, and [itex]k[/itex] is the (spatial) curvature of the universe.

Scientists
Alexander Friedmann (Фридман) (1888-1925)
Georges Lemaître (1894-1966)
Howard Percy Robertson (1903-1961)
Arthur Geoffrey Walker (1909-2001)

Recent forum threads on FLRW metric
 
Breakdown
Physics
> Astro Cosmo
>> Cosmology

See Also

Images

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.