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# Questions tagged [curvature]

Use this for questions pertaining to curvature of manifolds. Does not need to be specific to general relativity, but also for curvature of e.g. a [tag:calabi-yau] manifold.

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### gravitational convergence of light

light has a non-zero energy-stress tensor, so a flux of radiation will slightly affect curvature of spacetime Question: assume a flux of radiation in the $z$ direction, in flat Minkowski space it ...
283 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 ...
446 views

### Why does the overhand knot jam but the figure-8 knot doesn't?

After tensioning a rope with an overhand knot in it, it is often very hard if not impossible to untie it; a figure-8 knot, on the other hand, still releases easily. Why is that so? Most "knot and ...
952 views

### How to show the Gauss-Bonnet term is a total derivative?

It is well-known that the Gauss-Bonnet term $$\mathcal L_G =R^2 -4 R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\tag 1$$ do not contributes to equations of motion when adding it to ...
154 views

### How will two equal discs, rotating with equal but opposite angular velocities and put on top of each other affect the spacetime “surrounding” them?

In this article the Ehrenhaft paradox is described. You can read in it that, according to Einstein's General Relativity (to which this paradox contributed), the spacetime around a rotating disc is non-...
348 views

### Mathematical expression of energy storage

I'm trying to develop an idea which is as follows. Put simply, imagine a flat sheet of material which, when distorted (I.e. curved in the third dimension) stores energy. Now, by calculating the ...
2k views

### How to prove that Weyl tensor is invariant under conformal transformations?

I need to verify that the solution for vanishing Weyl tensor is conformally flat metric $g_{\mu\nu} = e^{2\varphi}\eta_{\mu\nu}$. The most convenient way to show this is to prove that Weyl tensor is ...
317 views

### Euclidean black hole extrinsic curvature

I have read that the extrinsic curvature at the horizon of a euclidean black hole is zero? Does anybody know how this can be shown?
60 views

### Are there any CMB-independant probes of the curvature of the Universe?

There is a preprint today (think it also appeared in Nature Astronomy on Nov 4) which argues that a $\Lambda{\rm CDM}+\Omega_k$ model with negative $\Omega_k$ fits the Planck Legacy 2018 CMB data ...