Unanswered Questions
1,969 questions with no upvoted or accepted answers
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What exactly is the relationship between the symplectic 2-form and the frequency of leaves of integrable systems in classical mechanics?
In classical mechanics we equip a differential manifold with a closed symplectic 2-form $\omega$. The symplectic leaves of integrable systems also have a unique frequency, in literature denoted $\...
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Does Hawking radiation need an apparent horizon and when does it switch on during stellar collapse?
I've read that Hawking radiation is implicitly linked with the existence of an apparent horizon (1). This seems a slightly less onerous than linking Hawking radiation with a genuine bona fide event ...
- 207k
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Why is the Ricci tensor diagonal for isotropic spacetime?
I'm reading Zee's Einstein Gravity in a Nutshell and while calculating the Ricci tensor for FRW spacetime he claims that because the spacelike slices of constant $t$ are rotationally invariant, the ...
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Derivation of the Hypersurface Deformation Algebra
Let $({M},{g})$ be a smooth $4d$ spacetime manifold with lorentzian metric $g$ and local coordinates $\xi^{\alpha}$ and let further $({N},{q})$ be a smooth $3d$ manifold with metric $q$ and local ...
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Angular momentum of vacuum solution in Einstein gravity
In Strominger's "Lecture Notes on Infrared Structure of Gravity", page 38, he mentioned about how part of this whole mess about "vacuum degeneracy" (classically, i.e. in the sense ...
- 1,752
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Does an evaporating black hole violate conservation of angular momentum?
Angular momentum is supposed to be conserved, but when a rotating black hole evaporates the Hawking radiation comes out in straight lines. Doesn't this violate conservation of angular momentum?
Does ...
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What is the difficulty in extending geometrodynamics to non-abelian fields?
In an attempt to widen my own horizons I've decided to educate myself in Wheeler's Geometrodynamics.
In the so-called "already unified theory" one can essentially reproduce an electromagnetic field ...
- 207k
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Hayden and Preskill's paper "Black holes as mirrors" - Classical model of black hole
If someone's read the "black holes as mirrors" paper by Hayden and Preskill which can be found here , Can you please explain to me how the probability of failure in the classical model of the black ...
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Metric transformation, polygons and gravitons
I'm trying to understand the paper by Hitchin called: ''Polygons and gravitons". I'm stuck at page 471.
At this point, he does some computations and obtains a metric:
$$
\gamma dz d\bar{z}+\gamma^{...
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Collapse of two large black holes in AdS
In $4d$ flat space, two black holes of mass $M$ can collapse to form another one of (roughly) mass $2M$. This process is spontaneous, as reflected by the fact that the black hole entropy $S=M^2$ ...
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Is there a null incomplete spacetime which is spacelike and timelike complete?
Geodesic completeness, the fact we can make the domain of the geodesic parametrized with respect an affine parameter the whole real line, is an important concept in GR. Especially, because the lack of ...
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Why is the Taub-NUT instanton singular at $\theta=\pi$?
Consider the following metric
$$ds^2=V(dx+4m(1-\cos\theta)d\phi)^2+\frac{1}{V}(dr+r^2d\theta^2+r^2\sin^2\theta{}d\phi^2),$$
where $$V=1+\frac{4m}{r}.$$
That is the Taub-NUT instanton. I have been ...
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Geometric entropy vs entanglement entropy (dependent on curvature coupling parameter)
I have a quick question. In hep-th/9506066, Larsen and Wilczek calculated the geometric entropy (which I believe is just another name for entanglement entropy) for a non-minimally coupled scalar field ...
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Correct statement of Birkhoff's theorem (spherically symmetric does not imply static?)
If I understand correctly, the appropriate statement of Birkhoff's theorem in general relativity is that
The Schwarzschild metric is the unique spherically symmetric vacuum
solution.
(Or we might ...
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Relation between maximally mixed state and thermal state
Hawking calculated the density matrix of the outgoing radiation to be a thermal state. I have heard people say this is a maximally mixed state. Is this because given a fixed average energy in the ...
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