Unanswered Questions
1,969 questions with no upvoted or accepted answers
29
votes
0
answers
745
views
Extended Born relativity, Nambu 3-form and ternary ($n$-ary) symmetry
Background: Classical Mechanics is based on the Poincare-Cartan two-form
$$\omega_2=dx\wedge dp$$
where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. On the other hand, the ...
- 1,064
18
votes
1
answer
2k
views
How to show the Gauss-Bonnet term is a total derivative?
It is well-known that the Gauss-Bonnet term
$$\mathcal L_G =R^2 -4 R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\tag 1$$
does not contribute to the equations of motion when adding it ...
CommunityBot
- 1
15
votes
0
answers
271
views
Is it known what the necessary and sufficient conditions are for the existence of a "3+1 split" (by means of a foliation) of a (Lorentzian) manifold?
When trying to do physics on a more general pseudo-Riemannian manifold we want to require that there is a foliation of this manifold into three-dimensional subspaces. By this I mean we would like to ...
- 7,776
14
votes
0
answers
311
views
What is the stringy interpretation of the cohomology classes arising from the Kähler class?
In superstring theory, one usually considers compactifications on Calabi-Yau 3-manifolds. These manifolds are in particular compact Kähler, hence possess a Kähler class which gives rise to nontrivial ...
- 16.4k
11
votes
0
answers
445
views
View of the sky from inside a black hole
Consider an observer located at radius $r_o$ from a Schwarzschild black hole of radius $r_s$. The observer may be inside the event horizon ($r_o < r_s$).
Suppose the observer receives a light ray ...
- 1,398
11
votes
0
answers
365
views
Significance for LQG of Sen's result on entropy of black holes?
Sen 2013 says,
...we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions [...] For Schwarzschild black holes in ...
CommunityBot
- 1
11
votes
1
answer
457
views
Aren't black holes required to exist forever in our frame of reference instead of evaporating?
I know that for an observer far away, nothing ever crosses a black hole horizon (due to time dilation), while in the frame of reference of a falling observer the horizon is nothing special on its way ...
- 2,083
10
votes
0
answers
271
views
Can you put the Spin Connection in block diagonal form? (to be applied to the Atiyah-Singer theorem)
I'm following the notes by Freed about the Dirac Operator. In section 5.4, equation (5.4.25-27), he makes the following claim about the Dirac operator. In a different notation than what he is using, ...
- 1,064
10
votes
2
answers
940
views
Conservation of Komar mass
The definition of Komar mass in GR is associated with one asymptotically flat end. However, a hypersurface may contain more than one end, such as the spacelike Einstein-Rosen bridge in Kruskal ...
CommunityBot
- 1
10
votes
0
answers
295
views
What really are exotic supersymmetric black holes?
I have just read (in the black holes chapter 14 on p244 of this book Ref.1) that in string theory, when one adds an (electric?) charge $Q$ to a static black hole, one can arrive at an exotic ...
- 756
10
votes
0
answers
500
views
Can a nearly-extremal black hole be stable against Schwinger vacuum breakdown?
I was doing some basic algebra to estimate the range of possible masses $M$ and electric charge $Q$ for a nearly extremal Reissner-Noström black hole. I want to see if the logic is correct
the ...
- 14.5k
10
votes
0
answers
259
views
Can we have consistent histories inside a black hole?
A consistent history is a POVM set of observables corresponding to a time-ordered product of projection operators. For gauge theories, not any old operator will do, only gauge-invariant observables. ...
- 3,745
9
votes
3
answers
332
views
Quantum pressure and chemical potential for a Schwarzschild black hole?
Just as Hawking showed that even Schwarzschild black holes have a temperature, shouldn't they also have a pressure and chemical potential? Are there any analytical formulae of those as well as
$$ T_{...
CommunityBot
- 1
9
votes
0
answers
1k
views
Weyl transformation vs diffeomorphism; conformal invariant vs general in/covariant
Background info:
My understanding:
1.
Weyl transformation is a local rescaling of the metric tensor
$$
g_{ab}\rightarrow e^{-2\omega(x)}g_{ab}
$$
A theory invariant under this Weyl transformation is ...
- 4,336
9
votes
0
answers
523
views
Objective time derivative that is not a Lie derivative
Summary
Led by an interest into the concept of "Material Objectivity", I am asking myself:
Are there objective time rates that are not Lie derivatives?
The long read
I am trying to understand the ...
CommunityBot
- 1
9
votes
0
answers
293
views
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 $\...
CommunityBot
- 1
9
votes
0
answers
262
views
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
9
votes
0
answers
779
views
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 ...
- 22.1k
8
votes
0
answers
454
views
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 ...
8
votes
0
answers
217
views
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
8
votes
0
answers
283
views
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 ...
- 358k
8
votes
0
answers
180
views
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
8
votes
0
answers
187
views
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 ...
- 1,222
8
votes
0
answers
215
views
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^{...
- 269
8
votes
0
answers
104
views
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 $S=M^2$ ...
8
votes
0
answers
291
views
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 ...
- 2,119
8
votes
0
answers
323
views
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 ...
- 6,067
8
votes
0
answers
343
views
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 ...
- 9,581
7
votes
0
answers
187
views
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 ...
- 684
7
votes
0
answers
291
views
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 ...
- 207k