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Spacetime line element to describe an expanding cube 
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#1
Nov2412, 10:15 AM

P: 46

Hi, I have to write a spacetime line element for the shape of a cube of cosmological dimensions. This cube is expanding like this:
i)With time, the cube becomes elongated along the zaxis, and the square xy 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! 


#2
Nov2912, 10:07 AM

P: 939

Spatially homogeneous means that your universe is translationinvariant. In other words, the metric cannot depend on x,y or z.
If the cube gets elongated in the zdirection, then you need at least two scale factors: one for z and one for x and y. 


#3
Nov2912, 01:52 PM

P: 669

[tex]\dot a > 0[/tex] 


#4
Nov2912, 02:41 PM

P: 46

Spacetime line element to describe an expanding cube
Ruta, I don't get why that line element satisfies the first condition. 


#5
Nov3012, 02:53 AM

P: 939

How would you know if something satisfies that condition? What does the condition mean, physically? 


#6
Nov3012, 06:05 AM

P: 46




#7
Nov3012, 08:59 PM

P: 669




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