All Questions
Tagged with scale-invariance general-relativity
11 questions
3
votes
1
answer
164
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Cyclic Universe Problems
In Penroses's hypothesis, at the end of each iteration the universe undergoes a conformal transformation, meaning distances are rescaled. If I am right, it implies that a planet from the previous ...
- 1,248
0
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0
answers
55
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Scale transformation of scalars in curved backgrounds
I am puzzled by the concept of scalar fields that arise in conformal field theory in curved backgrounds. In general relativity, so far as I understand it, a scalar field is basically a function ...
- 119
1
vote
2
answers
142
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Does the stress energy tensor scale with the metric tensor?
Question
I had some thoughts from a previous question of mine.
If I have a metric $g^{\mu \nu}$
$$g^{\mu \nu} \to \lambda g^{\mu \nu}$$
Then does it automatically follow for the stress energy tensor $...
- 1,349
0
votes
1
answer
239
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Scale invariance in curved spacetime?
Question
What does it mean for the metric to be scale invariant in curved spacetime (in the sense when I say a property is scale invariant in thermodynamics)? I'm confused as to how to define this. It ...
- 1,349
0
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1
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127
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How to amend General Relativity to include a position-dependent gravitational 'constant' $G$?
What is the best way to amend General Relativity to include a variable gravitational 'constant' $G$, that depends on the positions of all other masses?
That is, if the amount of 'bending of space-time'...
- 13.8k
1
vote
1
answer
400
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Another static solution of the Friedmann equations - interpretation of $p=-\rho c^2$
Looking for solutions of the Friedmann equations
$$(\frac{\dot a}{a})^2+\frac{kc^2}{a^2} = \frac{8 \pi G \rho+\Lambda c^2}{3}, \tag{1}$$
$$\frac{\ddot a}{a} = \frac{-4 \pi G}{3} (\rho + \frac{3p}{c^2})...
- 13.8k
3
votes
3
answers
625
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What are the implications of the scale invariance of the geodesic equation?
The geodesic equation in general relativity is famously invariant under affine reparametrization, i.e., under the reparametrization $\tau \to a\tau + b$ where $\tau $ is the proper time. This can be ...
user87745
9
votes
1
answer
595
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What sets the scale of a free Maxwell theory in $d\neq 4$?
The action for the free Maxwell theory is given by $$S=\int d^dx\sqrt{-g}\bigg(-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}\bigg)$$
The theory is invariant under conformal transformations $g_{\mu\nu}\to\Omega^2(x)...
user87745
2
votes
1
answer
191
views
Importance of Tracelessness of Tensor?
What makes the trace-free tensor (or part of it) so important?
As in trace-free Ricci tensor or Weyl tensor.
- 77
4
votes
1
answer
524
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Is a universe without massive particles scale-invariant?
In a popular talk by Roger Penrose about spacetime geometry, when introducing his conformal cyclic cosmology starting at 17:15 I think he says that as soon as there are no massive particles left in ...
- 9,444
11
votes
1
answer
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Is John Nash's "Interesting Equation" really interesting?
As recently mentioned in the news, before his passing, John Nash worked on general relativity. According to the linked article John Nash's work is available online from his webpage.
His work is ...
- 10k