Exploring FRW Symmetry to Geometrical Patterns in FRW Metrics

[TrickyDicky]

Does anybody know what kind of geometrical symmetry FRW metrics present? I know it's not spherically symmetric, but I think I recall having read it shows radial symmetry.

 

[Mentz114]

Does anybody know what kind of geometrical symmetry FRW metrics present? I know it's not spherically symmetric, but I think I recall having read it shows radial symmetry.

Isotropy and homogeneity. No special direction, and no special place. Geometrically it depends which coordinate chart you use.

 

[TrickyDicky]

Geometrically it depends which coordinate chart you use.

I thought the symmetry in a manifold (like spherical symmetry in Schwarzschild manifold for instance) was not dependent on the coordinate chart choice. Maybe you mean what FRW specifically I refer to, let's say the one with flat 3-space.

 

[TrickyDicky]

Isotropy and homogeneity.

Mentz, that would be the spatial component only, right? I meant the whole spacetime FRW manifold.

 

[Mentz114]

Mentz, that would be the spatial component only, right? I meant the whole spacetime FRW manifold.

Homogeneity requires that the gravitational field should be the same everywhere, so g₀₀ cannot depend on the position. Also the matter density should not depend on position. The (only?) metrics that satisfy this have the form given here
http://scienceworld.wolfram.com/physics/Robertson-WalkerLineElement.html.

Also see
http://www.phys.washington.edu/users/dbkaplan/555/lecture_03.pdf.

 

[micomaco86572]

Does anybody know what kind of geometrical symmetry FRW metrics present? I know it's not spherically symmetric, but I think I recall having read it shows radial symmetry.

Why isn't the FRW metric spherically symmetric?
Is it one of the maximally symmetric metric of 4D space-time?

thx

 

[WannabeNewton]

Why isn't the FRW metric spherically symmetric?

The space - like hypersurfaces are, just not the entire manifold.