So in deriving the metric, the space-time can be foliated by homogenous and isotropic spacelike slices.(adsbygoogle = window.adsbygoogle || []).push({});

And the metric must take the form:

##ds^{2}=-dt^{2}+a^{2}(t)\gamma_{ij}(u)du^{i}du^{j}##,

where ## \gamma_{ij} ## is the metric of a spacelike slice at a constant t

QUESTION:

So I've read that:

1) Homogenity would be broken if the a(t) was taken outside the metric

2) By isotropicity there can be no cross-terms dtdx, dtdy, dtdz.

What I know:

homogenous means the same throughout - translationally invariant.

isotropic means the same in every direction - rotationally invariant.

But I'm struggling to see how 1) and 2) follow from this. As stupid as it sounds, I dont really see where time comes in when these properties are only on the spacelike slices.

Cheers.

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# Isotric an homogenous implied form of FRW metric

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