All Questions
27
questions
4
votes
1
answer
209
views
Is gravitational particle production due to symmetry breaking?
A well-known fact about QFTs in curved spacetimes is that there is a phenomenon of particle production in expanding universes, these being described by the line element $$ds^2=-dt^2+b^2(t)d\vec x^2.$$
...
- 503
2
votes
1
answer
78
views
Why must the components $g_{0i}$ of an isotropic, homogeneous spacetime metric vanish?
In Daniel Baumann's book on Cosmology, it says that the metric of an isotropic, homogeneous spacetime must have the form $$\mathrm{d}s^2=-\mathrm{d}t^2+a^2(t)\gamma_\mathrm{ij}(x)\mathrm{d}x^\mathrm{i}...
- 1,187
0
votes
0
answers
44
views
Effects of anisotropy and non-homogeneity in the universe's symmetries...?
I was reading Philip W Anderson's essay "More is Different" (https://www.tkm.kit.edu/downloads/TKM1_2011_more_is_different_PWA.pdf) and at some point he links the isotropy and homogeneity of ...
- 2,462
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
4
votes
1
answer
180
views
How does spatial homogeneity make sense in general relativity?
Homogeneity of space implies that the laws of physics are form invariant under translations $(x, y, z)\rightarrow (x+a, y+b, z+c)$. This makes sense for Newtonian mechanics and special relativity.
...
- 8,640
1
vote
0
answers
101
views
(Wald's GR book) Isotropy implying constant curvature
Context
In Wald's GR book, p. 94 of chapter 5, he gives an argument for why isotropy and homogeneity implies constant curvature.
In summary, it goes like this: We can take the induced metric, $h_{ab}$,...
0
votes
1
answer
441
views
Understanding Killing vectors of FLRW metric
I am trying to understand how to calculate the Killing vectors of FLRW metric
\begin{equation}
ds^2 = dt^2 - R(t)^2\left( \frac{dr^2}{1 - k r^2} + r^2 d\theta^2 + r^2 \sin\theta d\phi^2\right).
\end{...
- 177
2
votes
1
answer
214
views
Killing tensor of Friedman-Robertson-Walker metric (not assuming flatness)
There exists an earlier question about how to verify that, if $U^\mu = (1,0,0,0)^\mu$ is the four-velocity of comoving observers, then
$$K_{\mu\nu} = a^2(g_{\mu\nu} + U_\mu U_\nu)\tag{1}$$
is a ...
- 1,215
-3
votes
1
answer
170
views
Must spacetime be homogeneous?
According to Einstein's equations of general relativity, space must be homogeneous. It can't have an edge or a centre. Is the same true of 4-dimensional spacetime – must it also be homogeneous?
- 371
1
vote
1
answer
135
views
Understanding the Plane Symmetric Metric
I don't understand as to what is the point of having a plane symmetric universe / metric at all? I mean shouldn't any physically sensical cosmological model (e.g. FLRW Model) entail a spherically ...
- 155
8
votes
3
answers
522
views
Why are particles described with Poincaré symmetry even though space seems inhomogeneous?
Poincaré transformation consists of translation, rotation, and boosting. And by assuming the physical quantities are invariant and equations are covariant under the transformations, we build the ...
- 479
0
votes
0
answers
149
views
Reparametrization invariance in FRW
It is usually pointed out that FRW metric is invariant under time reparametrization. Consider the flat case for simplicity
$$ds^2=N(t)^2dt^2-a(t)^2dr^2-a(t)^2r^2d\Omega^2$$
The choice of function $N(...
- 101
3
votes
1
answer
206
views
Is this the Melvin metric (magnetic universe) in disguise?
I'm solving the Einstein equation assuming a cylindrical symmetry and found something interesting which I never saw elsewhere. I now feel that I may have found the Melvin magnetic universe solution ...
- 7,592
1
vote
1
answer
305
views
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