All Questions
28
questions with no upvoted or accepted answers
3
votes
0
answers
88
views
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
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
3
votes
1
answer
208
views
Full Bondi-Metzner-Sachs (BMS) or asymptotic group are the same and have equal interpretations?
I had red about supertranslations or even superrotations. But I just discovered there are also superboosts and superLorentz ( I suppose this is for superrotations and superboosts).
Is the full BMS ...
- 6,611
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
2
votes
0
answers
93
views
General relativity in three spacetime dimensions and maximally symmetric spacetimes
Starting from Einstein's equations in $n$ spacetime dimensions with cosmological constant $\Lambda$:
$$R_{\mu\nu}+\left(\Lambda-\frac{R}{2}\right)g_{\mu\nu}=0,$$
one can that, by contracting both ...
- 1,044
2
votes
1
answer
538
views
Deriving the Minkowski Metric from homogeneity of space-time and the isotropy of space
In this wikipedia page, it says that one can derive the spacetime interval between 2 arbitrary events from the second postulate of special relativity, together with the homogeneity of spacetime and ...
- 504
2
votes
0
answers
186
views
Spacetime as a coset of a symmetry group
In the introduction to his nice PNAS paper on symmetry, David Gross said
Einstein’s great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of ...
user99292
2
votes
0
answers
233
views
Examples of manifolds (not) being: flat, homogeneous and isotropic
I am looking for (at least) one example of the following manifolds:
Flat, homogeneous and isotropic
Curved, homogeneous and isotropic
Flat, non-homogeneous and isotropic
Flat, homogeneous and non-...
user17116
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
1
vote
0
answers
62
views
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
vote
0
answers
57
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
1
vote
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
0
answers
159
views
Abel deprojection formula in static and spherically symmetric spacetimes
Given a fluid spherically distributed with density $\rho(r)$ in 3-dimensions in flat-spacetime; the projected surface density $\sigma(R)$ (onto two dimensions) can be obtained by the well known ...
1
vote
1
answer
108
views
Correlation between velocity and homogeneity of spacetime and isotropy of space
Considering only inertial frames of reference and constant velocities, does the fact that any velocity, with the exception for the speed of light in a vacuum, can be transformed, via an accurate ...
- 145
1
vote
1
answer
69
views
Properties of space-time intervals derived by symmetry principles
In many books about special relativity I found the following arguments:
1) because the transformations between two inertial reference frames $K$ and $K'$ are linear and because if $\Delta s^2 = 0 $ ...
- 433