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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0answers
30 views

Is gravitation a fundamental interaction between mass and spacetime? [on hold]

Please explain in detail about the nature of gravitation as a fundamental interaction.
-4
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0answers
34 views

The Sun's space-time warp [on hold]

Can we infer that the skin of the Sun is (to some depth) blanketed by the space-time warp created by its own mass? Does the Earth's mass create any measure of a space-time warp?
8
votes
3answers
5k views

Radius of curvature

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 ...
3
votes
2answers
106 views

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 ...
0
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0answers
30 views

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 ...
-1
votes
2answers
78 views

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?
2
votes
2answers
183 views

Hawking Radiation and Curvature

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 ...
3
votes
1answer
56 views

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 ...
3
votes
3answers
181 views

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?
3
votes
1answer
39 views

$f^{\prime}(R)=0$ 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 ...
0
votes
3answers
61 views

Space time curvature and gravity [duplicate]

Is Space time curvature responsible for gravity or Gravity responsible for the curvature in space-time.
1
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1answer
45 views

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?
3
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3answers
133 views

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 ...
0
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0answers
37 views

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 ...
2
votes
2answers
3k views

Radius of curvature and focal length

Is the radius of curvature of a convex or concave lens longer than the focal length of the lens? Does the center or curvature affect the focal point in a lens?
5
votes
1answer
46 views

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 ...
2
votes
1answer
357 views

Higher-Dimensional Metrics in (Hyper)-Spherical Coordinates

I want to compute the components of the Riemann curvature tensor (for a case similar to the Schwarzschild solution) in 4 + 1 dimensions, but I want to use a higher-dimensional analogue of spherical ...
1
vote
2answers
61 views

Pendulum on a train

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 ...
1
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0answers
62 views

Relation between second covariant derivative of Killing vector and Riemann tensor [closed]

I need to prove that $$D_\mu D_\nu \xi^\alpha = - R^\alpha_{\mu\nu\beta} \xi^\beta$$ where D is covariant derivative and R is Riemann tensor. $\xi$ is a Killing vector. I have proved that $$D_\mu ...
3
votes
2answers
89 views

Gravity and spacetime bending [duplicate]

Something that puzzles me if gravity is just bending of space time near a mass then what is gravitational force? If say two massive bodies were perfectly at rest relative to each other they would ...
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votes
1answer
39 views

Do we exist in warped space and time?

Does the Suns altering of space and time (as evidenced at an eclipse) extend to the Earth such that we exist in warped space and time or are we outside those effects.
0
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0answers
18 views

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 ...
-1
votes
2answers
36 views

Curvy space in and around massive objects [closed]

If space curves around massive objects, what happens to the space within the massive objects?
0
votes
0answers
42 views

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 ...
1
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1answer
45 views

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 ...
2
votes
1answer
124 views

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 ...
3
votes
2answers
145 views

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 ...
0
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0answers
15 views

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 ...
1
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3answers
87 views

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.
12
votes
3answers
1k views

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 ...
1
vote
1answer
64 views

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: ...
1
vote
1answer
62 views

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 ...
0
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0answers
33 views

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 ...
1
vote
1answer
76 views

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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votes
2answers
448 views

Space-time hospitality

Are there any reasons to assume that organic processes cannot arise in relatively flat spacetime environments? An argument for the existence of a critial value or window.
1
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1answer
67 views

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 ...
0
votes
1answer
48 views

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 ...
2
votes
2answers
57 views

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 ...
6
votes
3answers
263 views

Why does the FLRW metric assume constant curvature?

So the FLRW metric takes the following form in reduced-circumference polar coordinates. $$\mathrm ds^2 = -c^2 \mathrm dt^2 + a^2(t) \left(\frac{\mathrm dr^2}{1 - k\, r^2} + r^2 (\mathrm ...
3
votes
5answers
160 views

Local inertial frame

In general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds. Let $\xi^{\alpha}$ the coordinates in the local inertial frame, so we get ...
0
votes
2answers
85 views

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 ...
1
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0answers
51 views

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 ...
4
votes
3answers
220 views

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 ...
0
votes
2answers
75 views

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 ...
2
votes
3answers
146 views

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 ...
1
vote
1answer
25 views

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 ...
0
votes
0answers
29 views

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 ...
3
votes
1answer
4k views

Earth curvature refraction for dummies

I keep being presented with 'earth curvature experiment' videos recently, by flat/concave earth advocates. It seems to be their favorite "evidence" that Earth is not spherical. Debunking this gets ...
3
votes
1answer
153 views

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 ...
1
vote
2answers
85 views

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 ...