Unanswered Questions
6,163 questions with no upvoted or accepted answers
29
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0
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745
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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 ...
28
votes
1
answer
1k
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Electric charges on compact four-manifolds
Textbook wisdom in electromagnetism tells you that there is no total electric charge on a compact manifold. For example, consider space-time of the form $\mathbb{R} \times M_3$ where the first factor ...
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 ...
15
votes
0
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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 ...
14
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0
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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 ...
12
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0
answers
2k
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Average force between two parallel finite wires with AC
Imagine 2 parallel antennas (wires) of equal length (a) with a distance r between them.
Both have AC currents with identical sine waveforms (equal frequencies and amplitudes). They are also in phase ...
11
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0
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612
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Special conformal transformations and image charges
Let us consider a grounded conducting sphere with radius $r$ and a point charge $e$ at a distance $R>r$ from the center of the sphere. For simplicity, we can choose the sphere centered at the ...
11
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0
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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 ...
11
votes
0
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365
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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 ...
11
votes
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 ...
10
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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, ...
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 ...
10
votes
0
answers
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 ...
10
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answers
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 ...
10
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0
answers
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. ...