All Questions
28
questions
1
vote
2
answers
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
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
3
votes
2
answers
162
views
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
2
votes
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
views
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
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
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
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
4
votes
2
answers
343
views
Are there types of spacetime that have no symmetries?
We derive the most basic laws of physics from several fundamental symmetries (those from Noether's theorems, gauge symmetries, Lorentz symmetry...). But are there any types of spacetime where no ...
- 2,462
2
votes
1
answer
119
views
Would something in the center of a supermassive shell be pulled apart or remain stationary?
Imagine a supermassive hollow shell in space, and also imagine there is an object at the center of this shell.
How does the force of gravity affect the body inside the shell?
My reasoning is that the ...
- 145
2
votes
1
answer
204
views
Are isometries really global symmetries?
On one hand, a spacetime $(M,g)$ with the Killing vector $\xi^\mu$ and $x^\mu(\tau)$ a geodesic, we can construct the quantity
$$Q = \xi_\mu \frac{dx^\mu}{d\tau}\tag{4.32}$$
that is constant along the ...
- 1,044
0
votes
2
answers
123
views
How can we physically determine the metric in SR? How can we physically determine a coordinate system where $g$ is diagonalized?
Here I'll use theoretical units with $c=1$. Suppose we are given two coordinate systems $(t, x)$ and $(\tilde{t}, \tilde{x})$, and suppose they are related by $t = \tilde{t} - \tilde{x}/2$ and $x = \...
- 8,640
0
votes
2
answers
326
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Is a static spacetime always spherically symmetric?
I'm a bit confused. In this question it is suggested that a static spacetime can be spherically asymmetric. A static spacetime is one for which the metric doesn't change in time. It's irrotational too....
1
vote
1
answer
153
views
Understanding Birkhoff's theorem
I was seeing the generalisation of Newton's shell theorem to GR, including the answer given here:
Is spacetime flat inside a spherical shell?, but I don't understand why proving that the metric inside ...
- 1,124