The curvature tag has no wiki summary.
11
votes
5answers
2k views
Laplace operator's interpretation
What is your interpretation of Laplace operator? When evaluating Laplacian of some scalar field at a given point one can get a value. What does this value tell us about the field or it's behaviour in ...
7
votes
1answer
153 views
Is spacetime flat inside a spherical shell?
In a perfectly symmetrical spherical hollow shell, there is a null net gravitational force according to Newton, since in his theory the force is exactly inversely proportional to the square of the ...
6
votes
3answers
194 views
Why Can We Observe Space Curvature / Warping At All?
I don't understand why we are able to see and measure curvature / warping of space at all.
Space as I understand it determines distances between objects, so if space were "compressed" or warped, ...
6
votes
2answers
354 views
How can a point-like particle “feel” gravity, if locally the curvature of spacetime is always flat?
I imagine a point-like particle can only experience the local properties of spacetime. But locally there is no curvature and no gravity, as it is often stated that
Locally, as expressed in the ...
6
votes
1answer
520 views
What is the stress energy tensor?
I'm trying to understand the Einstein Field equation equipped only with training in Riemannian geometry. My question is very simple although I cant extract the answer from the wikipedia page:
Is the ...
6
votes
3answers
694 views
Does the curvature of spacetime theory assume gravity?
Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form "gravity wells." Objects which are ...
6
votes
1answer
165 views
Curvature of the Universe imaginary?
If the curvature of the universe is zero, then $$Ω = 1$$ and the Pythagorean Theorem is correct. If instead $$Ω> 1$$ there will be a positive curvature, and if $$Ω <1$$ there will be a negative ...
5
votes
1answer
114 views
Source term of the Einstein field equation
My copy of Feynman's "Six Not-So-Easy Pieces" has an interesting introduction by Roger Penrose. In that introduction (copyright 1997 according to the copyright page), Penrose complains that Feynman's ...
5
votes
2answers
200 views
Is the curvature of spacetime invariant? Could it be characterized as the ether?
I'm writing a paper for a Philosophy of Science course about GR/SR and I'm wondering if I can (1) characterize the curvature of spacetime as invariant and (2) argue that this is what Einstein referred ...
5
votes
1answer
156 views
Curvature and edge state
If the boundary of quantum hall fluid has non-constant curvature, how will it affect the edge state which is usually described in chiral Luttinger fluid?
4
votes
3answers
138 views
How do you tell if a metric is curved?
I was reading up on the Kerr metric (from Sean Carroll's book) and something that he said confused me.
To start with, the Kerr metric is pretty messy, but importantly, it contains two constants - ...
4
votes
2answers
207 views
Space-time geometry and metric
I am confused in one question in general relativity, why we can always express a space-time geometry only by metric. It means a metric, which is just about distance in tangent space, can tell us all ...
4
votes
3answers
113 views
How scalar curvature of following spacetime can be equal to zero?
For an interval of this spacetime,
$$
ds^{2} = c^{2}dt^{2} - c^{2}t^{2}(d \psi^{2} + sh^{2}(\psi )(d \theta^{2} + sin^{2}(\theta )d \varphi^{2})),
$$
scalar curvature is equal to zero. Also, Ricci ...
4
votes
2answers
79 views
How is the shape of the universe measured by scientists?
I would like to learn how scientists go about measuring the large-scale curvature of the universe to determine if the universe is closed 'i.e. spherical', flat, or open 'i.e. saddle shaped'.
My ...
4
votes
2answers
183 views
What is the variation of Gauss-Bonnet term a total derivative of?
What is the variation of Gauss-Bonnet term total derivative of?
i.e. Variation of Gauss-Bonnet combination $= \nabla_{\mu} C^{\mu}$.
What's $C^{\mu}$ in 4-dimensions?
4
votes
1answer
141 views
Does the curvature of space-time cause objects to look smaller than they really are?
What's the difference between looking at a star from a black hole and looking at it from empty space?
My guess is that the curvature of space-time distorts the wavelength of light thus changing the ...
4
votes
0answers
57 views
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 ...
4
votes
0answers
94 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 ...
3
votes
2answers
370 views
Where do I start with Non-Euclidean Geometry?
I've been trying to grok General Relativity for a while now, and I've been having some trouble. Many physics textbooks gloss over the subject with an "it's too advanced for this medium", and many ...
3
votes
2answers
222 views
asymptotic curvature of the universe and correlation with local curvature
There is not-so-rough evidence that at very large scale the universe is flat. However we
see everywhere that there are local lumps of matter with positive curvature. So i have several questions ...
3
votes
4answers
316 views
Gravitation is not force?
Einstein said that gravity can be looked at as curvature in space- time and not as a force that is acting between bodies. (Actually what Einstein said was that gravity was curvature in space-time and ...
3
votes
1answer
149 views
Curvature, Omega, the Flatness problem, and the evolving shape of the universe
I'm a little confused by this:
http://en.wikipedia.org/wiki/Flatness_problem
Which seems to imply the universe is more curved now than it was soon after the Big Bang. Look at the graph on the right ...
3
votes
2answers
92 views
How/why can the cosmic background radiation measurements tell us anything about the curvature of the universe?
So I've read the Wikipedia articles on WMAP and CMB in an attempt to try to understand how scientists are able to deduce the curvature of the universe from the measurements of the CMB.
The Wiki ...
3
votes
1answer
117 views
Material strain from spacetime curvature
Let's say that you moved an object made of rigid materials into a place with extreme tidal forces. Materials have a modulus of elasticity and a yield strength. Does the corresponding 3D geometric ...
3
votes
2answers
82 views
How can I vizualize and understand curved spaces in general relativity?
I'm taking a basic physics class and the teacher described space with a special table that has curves and black holes etc. He would throw a metal ball down onto it and the class would watch it circle ...
3
votes
0answers
67 views
Curvature and spacetime
Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a ...
2
votes
1answer
173 views
Difference between $\partial$ and $\nabla$ in general relativity
I read a lot in Road to Reality, so I think I might use some general relativity terms where I should only special ones.
In our lectures we just had $\partial_\mu$ which would have the plain partial ...
2
votes
2answers
114 views
What is the curvature of the universe?
What is currently the most plausible model of the universe regarding curvature, positive, negative or flat?
(I'm sorry if the answer is already out there, but I just can't seem to find it...)
2
votes
2answers
122 views
Curved space or curved spacetime?
As I understand it, you can have time + flat space = curved spacetime.
So, when one is trying to emphasise that there is a curvature to the space, is it more technically correct to say curved space ...
2
votes
1answer
78 views
Flat poster on a wall gaining curvature over time
Assuming you have a flat poster with no curvature, why is it that when you pin it to the wall (with thumbtacks) it gains curvature as seen in the picture below. When I put the poster up it was ...
2
votes
2answers
254 views
Equation of the saddle-like surface with constant negative curvature?
What is the equation for the saddle-like 2d surface (embeded in 3d Euclidean space with cartesian coordinates x, y and z) with constant negative curvature frequently used to illustrate open universe ...
2
votes
1answer
202 views
What bends fabric of space-time?
I know that mass can bend fabric of space-time, which causes gravity by making an object curve around a planet or star but is there anything else that can bend it?
Other energy sources, forces ...
2
votes
1answer
327 views
$\pi$ and the Curvature of Space
If one draws a circle on a sphere and measures the ratio of the diameter to the circumference, that value varies depending on the diameter of the circle compared to the diameter of the sphere it is ...
2
votes
1answer
148 views
What's the difference between the equivalence principle and curvature of spacetime?
Calculating using the equivalence principle only accounts for half the deflection of light, whereas the other half is from curvature of space-time.
But isn't the equivalence principle the same thing ...
2
votes
2answers
140 views
Galilean transformations and Frenet Frame
How I can prove that the curvature and torsion of a curve are invariant under the Galilean transformations? In my physics book a hint is the isometries of Galilean transformations, but it's still ...
2
votes
1answer
145 views
Curved lines in a picture (Photography)
My problem is when I take a picture (a close one) the straight edge looks a little curved. In a standard camera, like a CyberShot.
I would like to know if there is some relationship between the ...
2
votes
0answers
275 views
de Sitter and anti de Sitter metric
Is the following correct for the distance $d$ from the origin $(0,0)$ to point $(t,x)$ in the 2-dimensional
de-Sitter and anti de-Sitter spaces? Here, $t$ is time and the distance may be called the ...
2
votes
1answer
280 views
Superposition of Ricci scalars [closed]
Suppose I have two point/line singularities in spacetime (what is important to me is that they are localized). Also suppose I have some fields in spacetime and that the two singularities interact with ...
2
votes
0answers
166 views
A question about surface tension of membranes and their curvature
I'm reading a review about membranes properties and I have reach a section about fluid membranes. The section discuss the principal curvatures ($c_1, c_2$) and the spontaneous curvatures ($c_0$). ...
2
votes
3answers
154 views
Why geometrically four acceleration is a curvature vector of a world line? And what is proper acceleration?
Why geometrically four acceleration is a curvature vector of a world line?
Geometrically, four-acceleration is a curvature vector of a world line.
Therefore, the magnitude of the ...
1
vote
1answer
66 views
Is there a formula to work out how much the fabric of spacetime bends?
From my knowledge, a big mass (planet star etc) can bend the fabric of spacetime. Is there a formula that we can use to work out how much it bends?
1
vote
1answer
189 views
In what way is the Riemann curvature tensor related to 'radius of curvature'?
In Misner, Thorne & Wheeler, they say, in their delightful 'word equations' that
$$\left(\frac{\mathrm{radius\,\, of \,\,curvature}}{\mathrm{of\,\, spacetime}}\right) = ...
1
vote
2answers
155 views
What is the Riemann curvature tensor contracted with the metric tensor?
Can the Ricci curvature tensor be obtained by a 'double contraction' of the Riemann curvature tensor? For example
$R_{\mu\nu}=g^{\sigma\rho}R_{\sigma\mu\rho\nu}$.
1
vote
1answer
103 views
What is the curvature scalar $\Psi_{4}$?
What is the curvature scalar $\Psi_{4}$?
Is it related to the scalar curvature $R$?
What does its real and imaginary parts represent?
1
vote
1answer
77 views
Ricci scalars for space and spacetime, local and global curvature
If Ricci scalar describes the full spacetime curvature, then what do we mean by $k=0,+1,-1$ being flat, positive and negative curved space?
Is $k$ special version of a constant "3d-Ricci" scalar?
...
1
vote
2answers
190 views
How to concile flat spacetime and big bang?
After reading How do we resolve a flat spacetime and the cosmological principle? I still remain perplex.
Please excuse my ignorance and try explaining to me :
I thought that basically, when we ...
1
vote
1answer
431 views
Is the curvature of space around mass independent of gravity?
Is the curvature of space caused by the local density of the energy in that area?Could gravity be a separate phenomenon only arising from the curvature of space? For instance if the density of energy ...
1
vote
2answers
89 views
Ricci tensor for a 3-sphere without Math packets
Let's have the metric for a 3-sphere:
$$
dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right).
$$
I tried to calculate Riemann or Ricci tensor's ...
1
vote
0answers
97 views
How to calculate Riemann and Ricci tensors for a sphere? [closed]
Let's have the metric for a sphere:
$$
dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right).
$$
I tried to calculate Riemann or Ricci tensor's ...
1
vote
0answers
25 views
How to prove the derive the expression for space part of Riemann tensor for homogeneous and isotropic space-time?
It's not a homework!!
For spheric, hyperbolic and flat case
$$
dl^{2} = R^{2}\left(d \psi^{2} + sin^{2}(\psi )(d \theta^{2} + sin^{2}(\theta )d \varphi^{2})\right),
$$
$$
dl^{2} = R^{2}\left(d ...
