# 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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### If massive gravitons fill 'empty' space and are displaced by matter then is curved spacetime the state of displacement of the gravitons? [on hold]

APS Physical Review D: Massive gravitons as dark matter and gravitational waves Precursor: Bigravitons as dark matter and gravitational waves The massive graviton is a viable candidate of dark ...
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### Interpreting the Kretschmann scalar

How do you interpret the Kretschmann scalar (in general relativity)? What can you tell from it? The Kretschmann scalar is defined as $$K = R_{abcd} R^{abcd}$$ where $R_{abcd}$ is the Riemann ...
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### What is the difference between intrinsic and extrinsic curvature? [migrated]

In general relativity, energy bends spacetime. However, this doesn't mean that a fifth dimension for spacetime to "bend into" exists." That is, spacetime isn't embedded in a higher dimensional space, ...
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### Curvature of Hilbert space

That may appear as a dumb question, but: Does Hilbert space have curvature, or is it a flat space? How and why?
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### Does curved spacetime change the volume of the space?

Mass (which can here be considered equivalent to energy) curves spacetime, so a body with mass makes the spacetime around it curved. But we live in 3 spatial dimensions, so this curving could only be ...
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### 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 ...
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### What is the fate of a hyper-sphere universe?

This PBS video postulates a positively curved universe which is in the shape of something the narrator calls a "hypersphere". http://youtu.be/AwwIFcdUFrE?t=6m33s Such a universe would have no edge, ...
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### What is the geometric explanation for why the interior angles of a triangle sum to 180 degrees in both Euclidean space and Minkowski spacetime?

Four-dimensional Euclidean space has the same topology and affine structure as Minkowski spacetime, though the two have different metric structures. Given that the interior angles of a triangle ...
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### General relativity applications other than gravity

Do the Einstein field equations successfully predict/describe physical processes other than gravitational ones?
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### Where does the idea gravity=curvature of spacetime really come from?

I have been searching for quite a while but mostly found the answer: Einstein's genius. Quite unsatisfactory. I know and understand that the idea gravity=curvature of spacetime works. Furthermore I ...
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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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### How energy would be consumed for bending spacetime?

If we could assume that relativity theory is correct about spacetime bending. Can we calculate energy used for moving 1 kg of object in 1 meter by changing the shape of spacetime (simulate gravity)? ...
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### Why Newton's gravitational constant remains unchanged in relativity though gravity is not a force?

I know that Einstein described gravity as a curvature of spacetime. So, It is not a "force" but why Einstein had to accept Newton's gravitational force constant?
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### What made Einstein think that gravity was caused by the curvature of spacetime?

What observation/thought experiment led him to think this?
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We know that the curvature of spacetime is gravity itself and it is not a force.so,why do we feel our weight in a curve spacetime but not in a straight(I mean not curve) space time like zero gravity ...
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### Why does two masses with energy attract each other?

I have heard that every mass attract another mass with a force directly proportional to the multiplication of their masses and inversely proportional to the square of distance between them, but newton ...
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### Gravity and circular logic [closed]

My research into gravity indicates that warped spacetime, with time as the major influence, is gravity. It also indicates gravity causes time dilation. Why is this not a circular argument. It is ...
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I have come across a question that asked me to find the radius of curvature of a projectile. As far as I know, the path of a projectile is a parabola and I have found mention of the radius of ...
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### Is this video's notion of general relativity correct? [duplicate]

In this video it explains the path of the apple in the general relativity version of gravity as being a straight line on a curved surface. Is this valid? Edit: this isn't a duplicate of the supposed ...
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### How does Einstein's curved space time produce acceleration in a free falling object? [duplicate]

I never really thought much about all of this before so I'm definitely a newbie. Please excuse my ignorance. If I understand what I have read so far: if spacetime is curved time would click by at a ...
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### What is more fundamental: Geometry and Topology or physical matter? [closed]

Since, there is always an interplay between gravity and the fabric of spacetime. I wonder which is more fundamental: Geometry and Topology or physical matter?
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From a simple point of view in GR/QM we take a virtual pair creation and presumable they reunite shortly in flat space-time probably representable by a space-time warpage that generates geodesic ...
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### How could the universe be hyperbolic if hyperbolic space isn't symmetrical?

In the 2-D projections of the shape of the universe shown here, we see that the flat universe and the spherical universe are perfectly symmetrical, so any triangle drawn anywhere on them will be the ...
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### Why does matter curve space time? [duplicate]

I am under the impression that Einstein never explains in his General Theory of Relativity, why matter curves spacetime; could explanations please be given?
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### $f^{\prime}(R)=0$ in $f(R)$ gravity

Suppose in a certain $f(R)$ gravity theory, $f^{\prime}(R)=0$ for some finite value of $R$. (e.g. let $f(R)=R+\alpha R^2$ with $\alpha<0$. $f^{\prime}(R)=0$ at $R=-\frac{1}{2\alpha}$.) Also ...
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### Space time curvature and gravity [duplicate]

Is Space time curvature responsible for gravity or Gravity responsible for the curvature in space-time.
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### Can the curvature of the Universe be a function of time?

Apologies for the repetition here, but can our Universe experience (either physically or mathematically) non-constant curvature that is a function of time?
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### Do gravitational waves affect light?

Gravity "bends" light, predicted with theory of relativity and subsequently observed: how does gravity and gravitational waves achieve this effect, and shouldn't this effect be present wherever there'...
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### What´s the physical foundation of the assumption that the curvature of spacetime can be quantised? [duplicate]

At the moment different paths (by percentual very few people in the world) are taken to arrive (that is, if an arrival exists) at a theory that can quantise the curvature of spacetime. Considering the ...
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### Did our Universe experience a curvature dominated phase?

So, my question is simple: did our Universe experience a curvature dominated phase? Or, rather, could our Universe have experienced a curvature dominated phase? This seems quite shruggish, at first ...
I've seen multiple questions about a pendulum on a train and most say to use $T = 2 \pi (L/F)^{1/2}$ and I have done this to compare the pendulum's periods before being on a train and then once its on ...