Unanswered Questions
3,551 questions with no upvoted or accepted answers
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
1
answer
350
views
What is the full algebra of BRST-invariant observables for general relativity?
The Hamiltonian formulation of general relativity - either in the ADM formalism or in Ashtekar variables - is straightforwardly a gauge theory. While the BRST formalism has primarily been developed to ...
CommunityBot
- 1
14
votes
0
answers
437
views
How to perform a derivative of a functional determinant?
Let us consider a functional determinant
$$\det G^{-1}(x,y;g_{\mu\nu})$$
where the operator $G^{-1}(x,y;g_{\mu\nu})$ reads
$$G^{-1}(x,y;g_{\mu\nu})=\delta^{(4)}(x-y)\sqrt{-g(y)}\left(g^{\mu\nu}(y)\...
- 3,691
12
votes
0
answers
402
views
Holonomy group of Schwarzschild spacetime, other interesting examples?
I'm teaching myself a little about holonomy groups in the context of general relativity. This paper by Hall and Lonie classifies a lot of the possibilities for simply connected spacetimes in 3+1 ...
12
votes
0
answers
1k
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Variation of the Einstein-Hilbert action in $D$ dimensions without the Gibbons-Hawking-York (GHY) term
Consider the standard Einstein-Hilbert action in $D \ne 2$ dimensions spacetimes :
\begin{equation}
S_{EH} = \frac{1}{2 \kappa} \int_{\Omega} R \; \sqrt{- g} \; d^D x,
\end{equation}
where $\Omega$ is ...
- 207k
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
274
views
Radiative equilibrium in orbit of a black hole
According to Life under a black sun, Miller's planet from Interstellar, with a time dilation factor of 60,000, should be heated to around 890C by blue-shifted cosmic background radiation.
How they ...
- 2,196
11
votes
0
answers
664
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What are Galileons good for?
Lately I've seen many papers (for example "The galileon as a local modification of gravity"; 292 total hits on the arXiv) on types of field theories known as Galileons, and I'm wondering ...
- 22.1k
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
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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
0
answers
543
views
What is the Chandrasekhar-Friedman-Schutz (CFS) instability, exactly?
I am confused as to what the Chandrasekhar-Friedman-Schutz (CFS) instability is, exactly.
It seems to refer to this paper by Chandrasekhar, but I do not think this paper covers the full instability. ...
- 5,078
10
votes
1
answer
3k
views
Lagrangian for Perfect fluid Stress-Energy tensor
The wiki article on the Einstein-Hilbert action for General Relativity says that the stress-energy tensor $T_{\mu\nu}$ is related to the Lagrangian of matter, $\mathcal{L}_M$, by
$$T_{\mu\nu}=-2\frac{\...
CommunityBot
- 1
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
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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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