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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Can everything be described without anything needing to actually “bend”?

Is space bending because gravity actually causes small particles to move differently? If large source of gravity is somewhere are particles extending towards it, creating a "bend" in space? So "bend" ...
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1answer
47 views

What force causes massive objects to bend space? [duplicate]

The visualization of gravity as shown by this video is pretty good at explaining how massive objects bend space, and such bending causes objects around it to fall towards it (a.k.a: gravity). ...
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1answer
36 views

Covariant derivative commutator on spinors [on hold]

What is this object $[\nabla_{\mu},\nabla_{\nu}]\epsilon$ in terms of curvature tensor $R_{\mu\nu}$? Where $\nabla_{\mu}$ is the covariant derivative on a four sphere and $\epsilon$ is spinor. PS: I ...
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0answers
76 views

The Riemannian Curvature in a solid sphere [migrated]

Is the Riemannian Curvature at the centre of a solid sphere zero?
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1answer
91 views

Curvature of spacetime and the equivalence principle

Assuming the Einstein equivalence principle, formulated as following: The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the ...
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2answers
83 views

Telling if geometry is curved without Riemann tensor

If you're only interested in telling whether a certain geometry is flat or curved, and you do not need to know in which way it is curved, do you still need the Riemann tensor? When I try to visualize ...
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2answers
49 views

Do Heavy objects like planets and stars create Curve in spactime fabric?

According to Newton moon revolves around the earth because of gravitational pull! But Einsteins quoted that its not the pull but Earth's mass creates a curve in spacetime and Moon revolves on the edge ...
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1answer
66 views

Does charge bend spacetime like mass? [duplicate]

Does charge bend spacetime like mass? I'm not asking if electromagnetic forces can be described geometrically, but if EM fields could correspond to particular curvatures of spacetime, like gravity ...
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2answers
136 views

Can anyone explain me how time can bend according to Einstein in simple way? [duplicate]

I am just 16 and curious to learn about Theory of Relativity. Can any one explain it simple enough for me to understand? I read that it is bending of time-space or space-time that causes gravity. How ...
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1answer
75 views

Symmetry of extrinsic curvature tensor

I am trying to solve following problem: In a spacetime of signature (+, −, −, −), let $$ u^au_a = 1, \quad A_{ab} = \nabla_cu_dh^c_{\; a}h^d_{\; b}, \quad h_{ab} = g_{ab} - u_au_b $$ Show that ...
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2answers
49 views

Human max speed in open space

Suppose you are an astronaut forgotten in the middle of nowhere, between our solar system and proxima centauri's. Now, you are out of fuel. I heard that with some kind of movements, someone in free ...
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3answers
803 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 ...
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2answers
111 views

Calculation of Einstein tensor for weak gravitational field

I am studying A First Course in General Relativity (2nd Ed.) by Bernard Schutz. I have some difficulty in deriving Eq.(8.32) on P.193, the form of Einstein tensor for weak gravitational field, which ...
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4answers
815 views

When space bends, what are the lines that are being bent?

In an electric field diagram, the lines represent the electrostatic force vector at the position. These lines are bent when you place a charge into the system. What is the equivalent description ...
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0answers
31 views

Zero mean curvature and maximal volume

I have a 1+1 asympotically flat spacetime system (spherical symmetry) for which I'm trying to find the hypersurface which maximizes the volume enclosed in a sphere of a given radius $r=R$. **It seems ...
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2answers
204 views

How can the universe be flat?

Okay, so I just want to clarify a few things. According to what I have read, we have measured the universe to be flat, and the shape of the universe is directly related to the mass-energy density. ...
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0answers
54 views

Is the Big Bang notion compatible with the flat space? (A problem with the **moment** of Big Bang, not with the place of it) [duplicate]

A passage from a paper: "If one imagines running the clock backward in time, any given region of the universe shrinks and all galaxies in it get closer and closer until they smash together in ...
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2answers
73 views

Different signatures

I was working out the christoffel symbols, once where the metric that I am using has (+---) signature and another time where it has (-+++) signature because two books had different signatures and I ...
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1answer
65 views

How are these two Riemann tensor equations equivalent?

Poisson in A Relativist's Toolkit defines the Riemann tensor as$$A_{\,;\alpha\beta}^{\mu}-A_{\,;\beta\alpha}^{\mu}=-R_{\phantom{\mu}\nu\alpha\beta}^{\mu}A^{\nu}.$$ Foster and Nightingale's A Short ...
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1answer
62 views

How can the D'Alembertian of a field be interpreted intuitively?

The D'Alembertian operator is defined as $$ \Box = g^{\nu\mu}\nabla_\nu\nabla_\mu $$ For the Minkowski metric in Cartesian coordinates that is $$ \Box=\frac{1}{c^2}\frac{\partial^2}{\partial t^2} - ...
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2answers
69 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 ...
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5answers
142 views

How to explain space-time curvature in two minutes? [closed]

How would you explain what is the curvature of space-time in a short period of time like 2 minutes to non experience people?
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1answer
31 views

Calculating curvature of spacetime when energy is present

I am only about half-way of studying SR and GR and I am not yet familiar with a formula to calculate the curvature of spacetime when energy is present. To be more specific, I want to calculate ...
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3answers
202 views

How does warped space actually look (visually)?

Recently, I was reading about space warping due to extreme gravity and at speeds approaching c, but in books, they always show space in 2D and depth to show space distortion. I was wondering how ...
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1answer
44 views

Light trajectory

We have observed stars where "we should not" Some people say that gravity can alter light trajectory. Some people say that gravity actually alter the space on which light travels. Which one is ...
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1answer
34 views

If there are any discernible effects of travelling through curved space..?

If one is on a spaceship traveling through a 'very' curved section of space-time, are there experiments one could perform on the ship that would reveal measurable differences between the very curved ...
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1answer
133 views

How warped spacetime bends trajectories of light and moving objects?

I fail to see why the light follows something like the blue line and not the green line on the attached image. Figure 1 - light bends around warped spacetime Afaik. something similar happens ...
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1answer
71 views

Commutator of Gauge Covariant derivatives

What is the physical meaning of $$ [D_{\mu}, D_{\nu}] ~\propto~ F_{\mu, \nu}, $$ where $D_{\mu}$ is the gauge covariant derivative and $F_{\mu,\nu}$ is the field strength? Is it just a definition? ...
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4answers
146 views

Any tips on evaluating Riemann tensor?

I am calculating the Riemann tensor for the Schwarzschild solution. I've calculated all 9 non-vanishing Christoffel symbols already. Now I need to evaluate the Riemann tensor and I find no easy way to ...
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4answers
111 views

How is gravity proportional to space-time curvature in the rubber-sheet analogy?

In General Relativity, Einstein established that gravity is due to the curvature produced by objects in space. We all know that gravity is proportional to mass. The picture Einstein painted looks ...
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0answers
28 views

FRW Metric maximally symmetric, derivation, $R=3K$ or $R=6K$ confusion, two different texts

I'm looking at Tod and Hughston Introduction to GR and writing the metric in the two forms; [1]$$ ds^{2}=dt^{2}-R^{2}(t)(\frac{dr^{2}}{1-kr^{2}}+r^{2}(d\theta^{2}+sin^{2}\theta d\phi^{2})) $$ [2] $$ ...
2
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1answer
721 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 ...
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0answers
174 views

Can the universe be round but still infinite?

Can the universe still be infinite in space if its curvature is > 1? Is a manifold of positive curvature necessarily compact? Does the Tarski paradox have any bearing on the finite or infinite ...
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1answer
72 views

The actual space curvature

What is the curvature of our physical space, according to the latest experimental data? I've found it somewhat difficult to find a definitive answer to the question, because the spacetime curvature ...
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3answers
314 views

How do we know dark matter isn't curved spacetime?

Could Dark Matter actually just be spacetime with curvature "leftovers" from the big bang or the inflationary epoch?
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2answers
111 views

Does mass curve space?

Just to be sure, according to the theory of General Relativity, my understanding is that mass curves space-time. My question is, can mass also curve space?
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2answers
124 views

Once I calculate the Riemann curvature tensor, what do I do with it?

I am considering the Schwarzschild metric. I have calculated my Christoffel symbols and am able to calculate the Riemann tensor (I think). In short, I have done a bunch of work to find this thing ...
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2answers
84 views

Schwarzschild: Proof that $\{r<2m\}$ is a black hole

I saw the following proof to show that $\{r<2m\}$ is a black hole in the Schwarzschild metric. Consider the Schwarzschild metric: $$ g=-V(r)\text d t^2 + \frac{1}{V(r)}\text d r^2 + r^2 \text d ...
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1answer
121 views

Can energy bend space? [duplicate]

I know mass bends the space around it and I also remember matter can be converted into energy and vice versa, so my question is: can energy interact with space in a similar fashion as matter does?
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1answer
68 views

Bianchi Identity using null tetrad

I'm currently looking at the Newman-Penrose Formalism, and trying to understand where there sets of equations come from. For that, I need to know how I can write the second Bianchi identity for the ...
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1answer
56 views

Weyl scalar calculation

I'm trying to compute Weyl scalars, but don't really understand the formulae for them, in the sense I don't understand how to compute them. Let's take ...
3
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0answers
70 views

Feynman Path integrals in space with holes in it [closed]

Feynman Path Integrals are a way of calculating the wave function of quantum mechanics. It usually integrates every possible path through all of space. I wonder if there is any study of Feynman path ...
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2answers
924 views

Radius of curvature of a lens

Is the radius of curvature of a lens correspond the the radius of the sphere in which the lens rises from?
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1answer
92 views

How can I use Einstein's field equations? [duplicate]

Every time I try to find the answer to this question I get redirected to different pages that ultimately do not end up answering my question. I have some understanding of Riemannian geometry but have ...
2
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1answer
107 views

How can I use Einstein's field equations to find the metric tensor? [duplicate]

I have watched and read a lot on the topic of General Relativity and the geometry behind it. I am confident that I can derive an approximation of the the stress-energy-momentum tensor with just the ...
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0answers
67 views

How does Einstein's gravity work? [duplicate]

I'm a chemistry student interested in physics. Hope the question doesn't sound funny. As opposed to Newton's gravity, which doesn't explain how gravity works, Einstein explained gravity as a result ...
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1answer
96 views

Why is space (almost) flat? Is it because masses are approximately homogeneously distributed? [duplicate]

The question I have is: Why is space (almost perfectly) flat in our neighbourhood? (I am disregarding the deviations due to the sun and the planets.) Is it correct to say that space is (almost) flat ...
2
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1answer
160 views

Is my diagram of spacetime curvature valid (relatively)?

I've been wracking my brain trying to understand what "curved spacetime" really is, and I think replacing one dimension with the time dimension then drawing the world-lines through time was the "aha!" ...
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4answers
152 views

What is the meaning of Einstein's field equation in terms of source and its effects on curvature?

The Einstein's Field Equation is $$R_{\mu\nu}-(1/2)g_{\mu\nu}R=-8\pi T_{\mu\nu},$$ where the left hand side is the curvature term and the right hand side is the source term (see, Hartle). Now, in the ...
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2answers
53 views

Does the value of the Ricci scalar determine the strength of the gravitational field?

If I was solving an equation that contains the Ricci Scalar, and I want to solve the equation in the strong and weak gravity regimes, is right to assume that $R>>1$ for first case and ...