# Tagged Questions

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### Positivity of Total Gravitational Energy in GR

I read the following statement in the introduction to an article: Over the last 30 years, one of the greatest achievements in classical general relativity has certainly been the proof of the ...
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### Where did Karl Schwarzschild derived his solution?

Does anyone know more about circumstances of Karl Schwarzschild at the Russian front in 1915 where he allegedly derived his famous solution of the Einstein equations (describing a black hole)? Sources ...
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### Ultracold atoms and General theory of Relativty

I am looking for good reviews for the subject of Ultracold atoms and it's application in test of General theory of relativity. I am planning to pick up this topic as a semester project, can somebody ...
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### Dimensional reduction and Schwarzschild solution

It is well-known that, given a Killing vector $\xi_\mu$ for a metric, this can be dimensionally reduced. This is exactly the case of the Schwarzschild solution due to the rotational symmetry. This ...
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### Linearizing Gravity to ${\cal O}(h^3)$

I've seen the action of linearized gravity in many places. We basically have {\cal L} \sim \frac{1}{G_N}\left( - \frac{1}{2}h^{\alpha\beta} \Box h_{\alpha\beta} + \frac{1}{4} h \Box h + {\cal ...
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### Reference request: FLRW with k>0, dust, and positive cosmological constant

The exact solution representing a FLRW universe with $k>0$ and dust (p=0), and $\Lambda=0$, is described by a cycloid. What is the exact solution for dust, in the presence of a positive ...
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### Time reversal symmetry and reversal of vectors

Firstly: I have been told that under time reversal transformations, i.e. $t\rightarrow -t$, vector fields must change sign. Why is this? I haven't found this in the literature, any references? ...
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I've been trying to grok General Relativity for a while now, and I've been having some trouble. Many physics textbooks gloss over the subject with an "it's too advanced for this medium", and many ...
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### Abstract Algebra in Relativity and Cosmology?

Is Abstract Algebra useful in theoretical Relativity and/or Cosmology? If so can anyone give me some examples or point me towards a good book with that emphasis if it is one? Thanks in advance.
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### Analyticity and Causality in Relativity

A few weeks ago at a conference a speaker I was listening to made a comment to the effect that a function (let's say scalar) cannot be analytic because otherwise it would violate causality. He didn't ...
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### Fourier Methods in General Relativity

I am looking for some references which discuss Fourier transform methods in GR. Specifically supposing you have a metric $g_{\mu \nu}(x)$ and its Fourier transform $\tilde{g}_{\mu \nu}(k)$, what does ...
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### Why is spacetime near a quantum black hole approximately AdS?

In this link, one of the answers contains the statement If you examine the space-time near a finite area quantum black hole, you will see an approximate AdS space. Presumably "approximate" ...
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### That 10km/day error predicted if GPS satellite clocks not corrected for relativity

Some authorities have stated publicly and without explanation that if the theories of Special and General Relativity were not taken into account in the design of the GPS (by building the satellite ...