Unanswered Questions
1,969 questions with no upvoted or accepted answers
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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 ...
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18
votes
1
answer
2k
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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 ...
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15
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0
answers
271
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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 ...
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14
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answers
311
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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 ...
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11
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0
answers
445
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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 ...
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11
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0
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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
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11
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1
answer
457
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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
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0
answers
271
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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, ...
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10
votes
2
answers
940
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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 ...
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10
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0
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295
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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 ...
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500
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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 ...
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10
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259
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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. ...
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9
votes
3
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332
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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
$$ T_{...
CommunityBot
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9
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0
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Weyl transformation vs diffeomorphism; conformal invariant vs general in/covariant
Background info:
My understanding:
1.
Weyl transformation is a local rescaling of the metric tensor
$$
g_{ab}\rightarrow e^{-2\omega(x)}g_{ab}
$$
A theory invariant under this Weyl transformation is ...
- 4,336
9
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523
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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
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9
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0
answers
293
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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 $\...
CommunityBot
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0
answers
262
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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 ...
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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
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answers
454
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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 ...
8
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0
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217
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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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0
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283
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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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8
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0
answers
180
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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 ...
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8
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0
answers
187
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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 ...
- 1,222
8
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0
answers
215
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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^{...
- 269
8
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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
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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 ...
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8
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0
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323
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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 ...
- 6,067
8
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0
answers
343
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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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7
votes
0
answers
187
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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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7
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0
answers
291
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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 ...
- 207k
7
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0
answers
186
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Can the Dirac quantization condition be derived within Lev Vaidman's formalism without gauge fields?
Textbooks often claim that phenomena like the Aharonov-Bohm effect require that any local formulation of quantum gauge theory use gauge potential fields. (It's also sometimes claimed that the A-B ...
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7
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292
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On Ricci flow and 'nonlinear relativistic heat equation
This is somewhat related to a previous question, but is different at the core.
I proposed a Relativistic Ricci flow equation that takes the form
$$\frac{\partial R}{\partial t} = \alpha \Box^2 R = -...
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7
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0
answers
147
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Resource Recommendation for black hole metrics in General Relativity
In classical textbooks for GR, Schwarzschild and Kerr spacetimes are adequately described. In which books or articles, it is mostly believed that Reissner–Nordstrom, Kerr–Newman, Schwarzschild–de ...
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0
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A Universal Upper Limit on Mass Within a Radius $R$?
Since the universe has a positive cosmological constant, there is an upper limit on the mass of the black holes as evident from the so-called Schwarzschild-de Sitter metric:
$ds^2 = -f(r)dt^2 + \...
CommunityBot
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7
votes
2
answers
703
views
Auto-parallel Transport or Principle of Extremum Action?
In an affinely connected spacetime with a metric compatible connection, the equation of the curve in which the tangent vector at each point is the result of the parallel transport of every tangent ...
CommunityBot
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7
votes
1
answer
468
views
Coupling a spinor field to a preexisting scalar field?
So I'm not a physicist, but I'm thinking about a mathematical problem where I think physical insight might be useful.
We're working on a Riemannian manifold $(M,g)$ (positive definite metric) with a ...
CommunityBot
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7
votes
0
answers
308
views
Is the $\alpha'$ expansion in string theory an asymptotic expansion?
The low-energy bosonic effective actions of string theory lead to Einstein-Hilbert gravity, along with scalars and $p$-form Maxwell fields. For example, the action for type IIA string theory is
$S = \...
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7
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0
answers
239
views
Is it possible to have fermions in Schwarzschild spacetime?
To my understanding Geroch proved that on 4-dimensional non-compact manifold a necessary and sufficient condition for a manifold to have a notion of spinors is to be parallelizabe .1 (General ...
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answers
260
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BTZ Black Hole Central Charge and Conformal Weight
I have been trying to reproduce a calculation (equation 4.12) in this paper http://arxiv.org/pdf/1107.2678v1.pdf by Carlip reviewing the derivation of the effective central charge of the BTZ Black ...
7
votes
0
answers
715
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The surface area to volume ratio of a sphere and the Bekenstein bound
I am trying to relate the surface-area-to-volume-ratio of a sphere to the Bekenstein bound. Since the surface-area-to-volume-ratio decreases with increasing volume, one would surmise that, per unit of ...
- 207k
7
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0
answers
233
views
Do semiclassical GR and charge quantisation imply magnetic monopoles?
Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how?
(I am not ...
CommunityBot
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6
votes
1
answer
117
views
How come the magnetic field disappears when a neutron star becomes a black hole, while the rotation remains?
The only question I found is this one, but this considers as non-rotating neutron star collapsing:
Our final and most comprehensive test is represented by the collapse to a BH of a magnetized ...
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6
votes
1
answer
182
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Thermodynamic inaccessibility and its consequences
Caratheodory's principle, namely, that in any neighborhood of an arbitrary equilibrium state there are states not accessible via adiabatic reversible path, leads to the existence of an integrating ...
- 5,909
6
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0
answers
262
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Why are there multiple universes in the Reissner-Nordström solution?
I am trying to make sense of the Penrose diagram of a non extremal Reissner-Nordström spacetime, that is, the solution with two horizons. The coordinates are
$$ v'=\text{exp}\left(\frac{r_+-r_-}{2r_+^...
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6
votes
0
answers
230
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Saddle point contributions to the gravitational path integral
In his lectures on black holes and quantum information, Tom Hartman states that the gravitational path integral can be approximated as
$$
Z(\beta) \approx \sum_{g_\text{cl}} e^{-I_E[g_\text{cl}, \phi]}...
- 141
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0
answers
75
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Improving physics simulation of black hole accretion disk?
I have recently been working on software which uses ray tracing/marching to render a black hole in the Schwarzchild metric. I've implemented most everything that I originally set out to do, and I am ...
6
votes
1
answer
451
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Covariant derivative of the vielbein determinant
The vielbein postulate says that
$$\nabla_\mu e_v^{\,a}=\partial_{\mu}e_\nu^{\,a}+\omega_{\mu\,\, b}^{\,\,a}\,e^b_\nu-\Gamma^\sigma_{\mu\nu}\,e^{\,a}_\sigma=0.$$
$\nabla$ is the coordinate covariant ...
CommunityBot
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6
votes
0
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151
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How does definition of event horizon imply that they are null?
I am familiar with the definition of a (future) event horizon as the boundary of the closure of the causal past of the future null infinity. I am aware that event horizons are null hypersurfaces -- ...
- 491
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201
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Is there a physical interpretation of Poincaré duality?
Is there a known interpretation of Poincaré duality in terms of a physical equivalence between (maybe topological) sectors of different (probably susy) quantum field theories?
Edit/update :
If on a ...
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6
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0
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107
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Writing the EL equations in the language of differential geometry
I want to explore generalised Noether currents obtained from $q$-form symmetries in an action.
The regular way we obtain Noether currents is fairly straightforward: We have a 0-form symmetry $\phi \to ...
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