All Questions
93
questions
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2
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133
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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 $\vec{a}$ ...
- 11.7k
1
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0
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54
views
Independence of Lagrange function from time and position
In Landau & Lifshitz "Mechanics", it is said that from the time/space homogeneity Lagrange function is independent from time/position. I always thought that homogeneity means that motion ...
- 39
3
votes
0
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88
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Intuition for the interior Killing vector fields in Schwarzschild?
The Schwarzschild metric represents a stationary (and static), spherically-symmetric, spacetime. These characteristics are manifested by the four Killing vector fields: one for time translation and ...
- 1,290
1
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0
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62
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Confused about spherically symmetric spacetimes
I'm following Schutz's General Relativity book and I am confused about his description and derivations of a spherically symmetric spacetime. I searched online and found that using Killing vectors is a ...
- 151
1
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0
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57
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What are Supertranslations and Superrotations in General relativity, and how does it inform us about a detector at null infinity?
How did I get here?
While drafting my question, I found this very similar question on our site.
Three days ago, I happened upon the concept of supertranslations and superrotations in General ...
- 246
0
votes
0
answers
63
views
Stationary, static and strictly stationary/static?
Consider spacetimes which are asymptotically flat at null infinity.
How to explicitly show that there exists a hyper-surface orthogonal killing vector field $k^{a}$ that is time-like everywhere in ...
- 21
2
votes
0
answers
82
views
Killing Tensors: What quantities do they preserve?
It is known that coordinate transformation generated by Killing vectors (KV) preserve the metric components, i.e. it generates an isometry transformation. Are there similar geometrical quantities that ...
- 1,752
3
votes
2
answers
163
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Static spacetime and metric invariance
I'm studying General Relativity using Ray D'Inverno's book "Introducing Einstein's relativity". I don't understand what the author writes in paragraph 14.3 ("Static solutions") ...
- 65
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1
answer
68
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Isotropy of space doubts
From the following image, why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we ...
1
vote
1
answer
174
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Homogeneity of space doubts [duplicate]
This question might have been asked so many times, but here we go again. I'm wondering what homogeneity of space means. All the descriptions say:
there's no special point in space, every point looks ...
0
votes
0
answers
14
views
Isotrophy length inside material
The word “isotropy” means the same in all orientations. Hence isotropic material has the same properties in all directions. If you choose any point inside the material, isotropic materials have the ...
- 525
0
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0
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31
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Clarifying the role of symmetry in operator/state transformation rules
In Chapter 3 of his fairly classic text on quantum mechanics, Ballentine talks about the relationship between symmetries of physical space and corresponding transformations (via unitary operators, per ...
- 1,095
2
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1
answer
143
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Question on Tolman-Oppenheimer-Volkoff (TOV) equation for time-dependent spacetimes [closed]
Is there a way to conceive a TOV equation, and therefore the stability analysis for a metric like:
$$ ds^2 = -dt^2 + a^2(t,r)\big(dr^2 + r^2d\Omega ^2\big)~?\tag{1}$$
- 3,085
1
vote
1
answer
167
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What does it mean that the metric is static?
I'm reading the paper Regular phantom black holes where in page 2 (left column) the authors write that "the metric is static where $A(\rho)>0$".
Does anyone know what they mean with the ...
- 2,478
2
votes
1
answer
100
views
Topological phase transitions for the whole universe...?
Physicist Grigory Volovik has put forward some ideas about the universe undergoing a topological phase transition (especially in the early stages of the universe). He published a book called "The ...
- 2,462
0
votes
0
answers
66
views
No symmetries in the universe at the Big Bang...?
I apologize in advance if this is a stupid question but...
According to some scenarios about the beginning of the universe (namely cosmological inflation), in layman terms, everything was born out of ...
- 2,462
2
votes
2
answers
175
views
Do the Klein bottle and torus topologies break the Lorentz invariance?
According to this preprint, it seems that there are topologies (like the Klein bottle and the torus) that break some symmetries (like the Lorentz and translation invariances).
Is this right? Can they ...
- 2,462
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
3
votes
2
answers
158
views
Are there non-smooth metrics for spacetime?
I found this statement in a discussion about the application of local Lorentz symmetry in spacetime metrics:
Lorentz invariance holds locally in GR, but you're right that it no longer applies ...
- 2,462
1
vote
1
answer
81
views
What if the universe was not uniform...?
In this popular science article, they say that if our universe resulted to be non-uniform (that is highly anisotropic and inhomogeneous) then the fundamental laws of physics could change from place to ...
- 2,462
0
votes
0
answers
87
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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
1
vote
1
answer
112
views
Symmetries changing depending on spacetime?
Just as the Lorentz symmetry holds globally in Minkowski spacetime, could the opposite also occur? That is, are there any spacetimes where the Lorentz symmetry would be broken (locally, not just ...
- 2,462
3
votes
1
answer
212
views
Is spacetime flat inside a rotating hollow sphere in general relativity?
Newton himself proved the Shell theorem, stating that inside a hollow sphere there is no gravitational force on a point mass. This theorem relies on the fact that Newtonian gravity falls off like $1/r^...
- 9,910
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1
answer
105
views
If the universe is infinite, would it be homogenous?
I know, that we can't really know the answer to that, but what is the current state of understanding?
We seem to assume that on very large scales, the universe is homogenous. As I understand it, this ...
- 866
1
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0
answers
50
views
Does a system with translational symmetry implies that space is homogeneous?
In my classical mechanics course, we sometimes described a system to have translational symmetry, and other times we said that it is homogenous in space and isotropic. While I know they are different, ...
- 31
1
vote
1
answer
136
views
Is the non-simply connected version of AdS space a maximally symmetric spacetime?
A common construction of anti-de Sitter space is the following:
Start with the flat five-dimensional manifold with metric $ds_5^2 = -du^2 - dv^2 + dx^2 + dy^2 + dz^2$.
Consider the hyperboloid ...
- 48.4k
0
votes
0
answers
42
views
Commutation relation of $P^{\mu}$ with fermion field $\psi(x)$
On Giunti and Kim's book "Fundamentals of neutrino physics and astrophysics", page 38-39, the book is trying to derive the commutation relation of $P^{\mu}$ and $\psi(x)$.
Begin with:
$$ U\...
- 1,421
0
votes
1
answer
121
views
Off-diagonal elements of the metric tensor and reversal symmetries
Given a metric that may be written as in some suitable coordinate system as $g_{\mu0}=\delta_{\mu0}$ and arbitrary other components, what properties of the spacetimes described by this kind of metric ...
- 103
1
vote
1
answer
90
views
How to map a complex plane Mobius transformation to 1+1D Minkowski real plane?
So consider the $(x,t)$ plane endowed with the minkowski metric, namely:
$$ds^2 = dx^2-dt^2.$$
It is well known that we can Wick rotate the time coordinate to get to the Euclidean metric. This can be ...
- 2,296