All Questions
93
questions
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2
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123
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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 $\vec{a}$ ...
- 11.8k
1
vote
0
answers
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
answers
87
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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
answers
55
views
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
60
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
158
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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
0
votes
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
171
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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
13
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
answers
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
votes
1
answer
142
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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
161
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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 ...
- 2,466