# Tagged Questions

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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### Is the fabric of space time a real thing? [duplicate]

With ny limited intelligence I think Einstein said that the gravity is caused by a curvature in spacetime.But unless there is an actual feelable fabric(or someting similar) how is a curvature caused ...
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### Curvy space in and around massive objects [closed]

If space curves around massive objects, what happens to the space within the massive objects?
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### Can a lightlike singularity have nonzero mass?

The effective mass of the Schwarzschild solution is valid at $r=0$. For $m>0$, we have a spacelike singularity, while for $m<0$ we have a timelike singularity. Suppose, instead of a spacetime ...
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### Small enough planet to notice rounding

This is my first question on Physics StackExchange, so bear with me. I am wondering. How dense would a planet need to be for a human to notice the fact that the planet is not flat, but round, by ...
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### Is every solution of Einstein field equations unique?

Einstein's equation is $$8 \pi T_{ab} = G_{ab},$$ where the left side contains the stress-energy tensor and the right side contains the Einstein tensor. Is there exactly one unique stress-energy ...
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### Is curvature space-time has impact on the object geometry

When we have e.g. metallic cube of dimensions 1x1x1m and we put it on the space without gravitational force the cube has equal 1x1x1m and we can use Euclidean geometry. But when this cube move on ...
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### How does curved space make an obejct move toward Earth? [duplicate]

I think I understand how the equivalence principle shows how light can bend and therefore space must be curved. What I do not understand is how curved space makes an object move directly toward the ...
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### How/why does gravity affect spacetime? [duplicate]

I've always heard that gravity warpes spacetime, but I've never understood why and/or how. I'm only 12 so please keep it simple if possible.
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### How does gravity truly work? [duplicate]

I Am only 12 years old and I'm constantly wondering and trying understand how gravity really works. On YouTube everyone always talks about objects wrapping space time around themselves and uses the ...
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### Extrinsic curvature components

I'm trying to understand how to derive the extrinsic curvature (in order to understand some calculation on fluid/gravity dynamics). But I hit a wall in my progress. I stuck at trying to verify the ...
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### Does mass compress space-time?

My understanding of relativity explains that the presence of mass warps space-time so that light travelling through the warp follows at straight line but the warp itself is curved and therefore the ...
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### Questions about how the curvature of universe is described with a single number

I often read of physics talking about "the" curvature of the universe, giving it some letter $K$, and claiming that we have seen that $K = 0$ within such and such certainty. I have three questions: ...
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### In General relativity, what is the meaning of flow of $x$ momentum in $x$ direction or pressure in $x$ direction? [duplicate]

I found this interesting paper on Arxiv devoted to explaining Einstein's field equations in simple English. The author, JC Baez, does this by considering a group of small spherical balls in ...
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### Could it be possible to bend space in more than one “way”?

Ever since the announcement of the discovery of gravitational waves, I have found myself pondering related notions of space. Recently, I was thinking about an analogy I've heard to explain how mass ...
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### How do you know what kind of space(time) you have when solving the Einstein Field Equations?

I'm experimenting with the EFE, and I ''invented'' a metric; a diagonal non-zero metric, and I discovered that the Riemann tensors are equal to zero which implies the Einstein tensor $G_{mn}$ equals ...
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### Metric defining an sphere [closed]

I want to find for which cases this metric can define an sphere: $$\frac{1}{P^2}\left(\mathrm d\theta^2+\sin^2 \theta\; \mathrm d\phi^2\right)$$ where $P=\sin^2 \theta+K\cos^2 \theta$, with $K$ the ...
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### How is the universe flat?

I have real trouble visualising what is meant by the descriptor 'flat' when referred to the shape of the observable universe. Which one of the below is more accurate? a) It is flat in a 2D way, like ...
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### Gravitational self-interaction

Today, someone asked me why "the warped space-time warps itself" (he read it in Kip Thorne's: The Science of Interstellar). I guess this is related to the gravitational self-interaction. But I don't ...
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### What parameters could be considered to measure the coiling of a ring?

I want to draw a phase diagram to quantify the coiling of a ring inside my system and I was wondering what parameters could be use to precisely define how coiled the ring is. Currently I am modeling ...
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### Space/time elasticity and state changing

What happens to a particular section of space/time that has been bent due to a large gravitational force that has passed it by? Does it "snap back" to it's original state. Is it permanently bent? Is ...
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### Why is the Ricci tensor defined as $R^\mu _{\nu \mu \sigma}$?

The Ricci tensor is defined as the contraction of the Riemann tensor in its upper and the second lower index. I was wondering why it is defined this way. What happens if the Ricci tensor is defined ...
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### Are gravitational waves effected by the curvature of space time (gravitational lensing)?

I have a basic question I can't seem to find anything on (I keep hearing about how gravity waves and gravitational lensing were both predicted by Einstein). We all know about the gravitational ...
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### General Relativity, Curvature, and extra dimensions

Setup of idea I had somewhat of a thought question regarding general relativity. Consider a simple situation of a sphere and arrow. You hold the arrow and walk from the equator to the north pole. ...
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### How does LIGO account for curvature of Earth?

Using an earth curvature calculator, I found that at a distance of 4 km (the length of LIGO's arms), more 1.26 m is hidden by the horizon. When constructing LIGO, did they account for the curvature of ...
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### Meaning of $R=0$, $R_{ab}=0$. $R_{abcd}=0$

First let me state some definition The Einstein tensor is given by \begin{align} G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R \end{align} and note that \begin{align} G^{\mu}_{\phantom{\mu} \...
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### Identity $\epsilon_{abcd} R^{cd}_{\phantom{cd}mn} = \epsilon_{mncd} R^{cd}_{\phantom{cd}ab}$ in vacuum

starting from \begin{align} \epsilon_{\rho\lambda\xi \kappa} R^{\xi \kappa}_{\phantom{ab} \sigma\tau} + \epsilon_{\rho\sigma \xi \kappa} R^{\xi \kappa}_{\phantom{ab} \tau \lambda} + \epsilon_{\rho \...
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### Why do we look at non-flat geometries in Cosmology?

In Cosmology we use the Robertson-Walker-Metric which follows from the cosmological principle & mathematics. This metric leaves three cases for a possible curvature (or geometry) of space (not ...
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### If gravity is due to curvature, how does gravity work in situations with no curvature?

The strength of the gravitational field falls off as the inverse square of the distance from a spherical source. It only falls off as the inverse of the distance from an extended cylindrical or line ...
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### Help with the Ricci tensor and Chistoffel Symbols [closed]

I really am confused with certain notations of the Ricci tensor and the Christoffel symbols. I'm looking to evaluate $R_{00}$ from my lecture notes, but I'm a little stuck at one point. The Ricci ...
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### Is there inflationary solution in $R^2$ theory in Jordan frame?

In the Starobinsky $R^2$ inflation model, one usually uses a conformal transformation from Jordan frame to Einstein frame in which the action can be written just like Einstein action + scalar field ...
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### Why is spacetime curved by mass but not charge [duplicate]

According to general relativity theory, the deformation of spacetime is proportional to energy tensor $$T_{\mu\nu}.$$ $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi G T_{\mu\nu}.$$ Does it mean that ...
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### Direction of Gravity [duplicate]

I ran into a pde that has a parameter in it that can be either $+1$ or $-1$. They say the $+1$ case corresponds to gravity pointing upwards, whereas the $-1$ case applies to gravity pointing downwards....
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### References to learn $f(R)$ gravity?

What reference(s) can I use to learn $f(R)$ gravity?
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### See behind the black hole

Why in this video does the 2nd black hole appears to change size and appear larger the farther away it gets? How can you see behind it? http://www.youtube.com/watch?v=ENd8Sz0AFOk
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### What exactly does the Kretschmann scalar implies and how does it work?

From the General Relativity class lectures I understood that this particular invariant, the Kretschmann scalar namely $$R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho}$$ is really important because, ...
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### How can I prove that for a Killing vector $\nabla^a \nabla_a \xi^\mu = -R^b_a \xi^a$? [closed]

I'm taking a course on General Relativity and I'm trying to prove that for a Killing vector field $\xi^\mu$ the following equation holds: $$\nabla^a \nabla_a \xi^\mu = -R^\mu_a \xi^a$$ Where $R_ab$ ...
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### Proper time and asymptotic flatness

I'm trying to understand the concept of asymptotic flatness in general relativity, and came up with the following question: If the proper time $\tau$ is infinite for a timelike geodesic, does it mean ...
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### How does bending in space-time caused by mass energy translate into acceleration of object? [duplicate]

Let say we have 2 similar apples separated by a distance apart, just their mass energy alone is sufficient to cause bending in the space-time. I think it is this bending in the space-time that cause ...
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### What allows us to assume spacetime is flat when no normal matter is present?

Dark matter causes a bend in spacetime. We see this through gravitational lensing. But what allows us to assume spacetime is flat when no normal matter is present? Why can't we say that dark matter ...
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### Why does the curvature of space decrease during inflation but increase after it?

According to the Friedmann equation, curvature of space will increase with time/expansion of space, but I've also read that during Inflation, the expansion caused the Universe to flatten out. What is ...
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### Stress-Energy Tensor of Riemann's Curvature Field

Einstein, in "The Foundation of the General Theory of Relativity," as well as most modern lecturers in the subject, use a pseudo-tensor for the stress-energy of the gravitational field. By ...
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### Gravity: Why Do things fall to Earth? [duplicate]

If gravity is in reality spacetime geometry why when I drop an object on the surface of the Earth does it fall to the ground? Does spacetime push it?
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### How does “curved space” explain gravitational attraction? [duplicate]

They say that gravity is technically not a real force and that it's caused by objects traveling a straight path through curved space, and that space becomes curved by mass, giving the illusion of a ...
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### Which tensor describes curvature in 4D spacetime?

I heard these two statements which don't work together (in my mind): In 4D spacetime the curvature is encoded within the Riemann tensor. He holds all the information about curvature in spacetime. ...