All Questions
7
questions
1
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2
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227
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Cosmology - Confusion About Visualising the Universe as the Surface of a 3-Sphere
Consider the FRW metric for the Universe in the form found in many standard cosmology textbooks:
$$ds^2 = -dt^2 + a(t)^2\left(\frac{dr^2}{1-Kr^2}+r^2(d\theta^2 + \sin^2\theta d\phi^2)\right)$$
I am ...
- 201
3
votes
2
answers
444
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What is the general form of the Friedmann-Robertson-Walker metric in 4D?
I have written in some old notes that the FLRW (also known as FRW) metric can be written as:
$$ds^2=dt^2 + a^2 (t) [dr^2 +r^2(d\theta^2 + sin^2\theta d\varphi ^2)] \tag{1}$$
I believe this is its ...
- 753
4
votes
1
answer
116
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Is there any "realistic" metric of type $\mathrm{(A)dS}_2 \times \mathcal{T}_2$ in General Relativity?
After studying the Bertotti-Robinson metric, which describes a $\mathrm{AdS}_2 \times \mathcal{S}_2$ universe, I was wondering about other kind of closed topologies with holes, like $\mathrm{(A)dS}_2 \...
- 7,592
1
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1
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305
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Cylindrical universe cosmology in general relativity
Is there a compact cylindrical universe solution to the Einstein equation, with space homogeneity, without using "artificial" periodic boundaries? I'm expecting a metric of the following shape:
\...
- 7,592
1
vote
1
answer
132
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What is this metric's scale factor?
While answering this question about a hypothetical 3-sphere universe $S^3$ expanding with a constant acceleration $\phi$ from a zero initial speed
$$ r=\dfrac{\phi}{2}t^2$$
I started from a generic ...
- 12.7k
12
votes
1
answer
356
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What are the allowed topologies for a FRW metric?
Given a spacetime that has the maximal amount of spacelike translations and rotations, what are the possible topologies it may take? I am mostly wondering about the "time" topology since the spatial ...
- 16.5k
1
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0
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343
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How to test that a flat metric represents a global three-torus geometry
When introducing Robertson-Walker metrics, Carroll's suggests that we
consider our spacetime to be $R \times \Sigma$, where $R$ represents the time direction and $\Sigma$ is a maximally symmetric ...
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