Hi, I have to write a spacetime line element for the shape of a cube of cosmological dimensions. This cube is expanding like this:(adsbygoogle = window.adsbygoogle || []).push({});

i)With time, the cube becomes elongated along the z-axis, and the square x-y shape doesn't change.

ii)The line element must be spatially homogeneus. (I dont know what this means).

I think there must appear the scale factor a(t) because of the expansion, but I don't know how to use the conditions of the expansion.

For a cilinder, I would use something like this: [itex]dS^2=-dt^2+a^2(t)(R^2 d\theta^2+dz^2)[/itex] where R is the radius of the cilinder.

Any help?

Thanks!

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# Spacetime line element to describe an expanding cube

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