All Questions
37
questions
1
vote
2
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133
views
Is the FRW metric, based on spatial homogeneity and isotropy, rotationally and translationally invariant? If so, how?
The spatial part of the Minkowski metric, written in the Cartesian coordinates, $$d\vec{ x}^2=dx^2+dy^2+dz^2,$$ is invariant under spatial translations: $\vec{x}\to \vec{x}+\vec{a}$, where $\vec{a}$ ...
- 11.8k
4
votes
3
answers
199
views
Change of variables from FRW metric to Newtonian gauge
My question arises from a physics paper, where they state that if we take the FRW metric as follows, where $t_c$ and $\vec{x}$ are the FRW comoving coordinates:
$$ds^2=-dt_c^2+a^2(t_c)d\vec{x}_c^2$$
...
- 293
2
votes
1
answer
134
views
How do you relate $\Omega_{k}$, the curvature term in the FLRW metric, to the radius of curvature?
I have assumed, for reasons a bit too detailed to go into here, that if $\Omega_{k}$, the curvature term in the FLRW metric, is equal to 1, then the radius of curvature is equal to 13.8 billion light ...
- 371
0
votes
0
answers
62
views
Spacetimes where symmetries vary from place to place?
Are there spacetimes or metrics where symmetries (like Poincaré, Lorentz, diffeomorphism, translational... invariances) are only local and the symmetries of one local neighbourhood are not, a priori, ...
- 2,462
0
votes
0
answers
86
views
Spacetimes, metrics and symmetries in the theory of relativity?
I was discussing this paper with a couple of physicists colleagues of mine (https://arxiv.org/abs/2011.12970)
In the paper, the authors describe "spacetimes without symmetries". When I ...
- 2,462
3
votes
1
answer
202
views
Penrose conformal diagram of Morris-Thorne wormhole
Consider the classical Morris-Thorne wormhole solution:
$$\tag{1}
ds^2 = dt^2 - dr^2 - (r^2 + a^2) \,d\Omega^2,
$$
where $a$ is a positive constant, $r > 0$ for one asymptoticaly flat spacetime, ...
- 7,592
1
vote
0
answers
49
views
Which class of metrics should I look at?
In the context of GR, I would like to consider a spherical body (or spherical inhomogeneity) with a time dependent energy-momentum tensor immersed in some fluid, for example radiation. So I am not ...
- 4,448
2
votes
0
answers
48
views
Does expansion of space over time assume a particular space/time dichotomy?
Regarding the expansion of the Universe, Wikipedia states:
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe ...
- 222
3
votes
2
answers
149
views
Does spacetime bending contradict the universe following euclidean geometry?
According to experiments the universe is believed to be flat, meaning that it would follow euclidean geometry. However, is that compatible with the fact that spacetime bends due to gravity? Does ...
- 31
0
votes
1
answer
375
views
Spacetime Diagram for Robertson-Walker Universe
For the Robertson Walker universe with metric
$$ds^2 = -dt^2 +a(t)[dx^2+dy^2+dz^2]$$
where $a(t)=t^q$ and $0<q<1$, the light cones in the spacetime diagram are drawn as follow:
From the diagram, ...
- 4,235
1
vote
0
answers
49
views
Present value of the cosmological scale factor, important or arbitrary?
I'm now confused about a subject that I thought was very clear to me, until recently. So I need to sort this clearly once and for all. Consider the standard FLRW cosmology in classical general ...
- 7,592
1
vote
2
answers
227
views
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
0
votes
1
answer
148
views
How do you find the proper separation between two spacetime points?
Suppose you had two points in space-time A and B, where A = (t1, χ1, θ1, φ1) and B = (t1, χ2, θ1, φ1). How would you use the FLRW metric to find the proper separation? In this case the points occur ...
0
votes
0
answers
45
views
Overcounting foliations in quantum cosmology?
Assume that we have states of 3-space with an intrinsic metric $h^{ij}$, and that we have already factored out equivalent 3-metrics.
In quantum cosmology, one might evolve a state with some intrinsic ...
user84158
1
vote
0
answers
58
views
Cosmology without introducing a metric in a manifestly diffeo-invariant way
I have a question that bothers me for quite some time:
Can cosmology be done without introducing a metric explicitly, and in a manifestly diffeomorphism-invariant way? Assuming that we are in the ...
- 696