Physics Stack Exchange
Physics Stack Exchange

Questions tagged [curvature]

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 Calabi-Yau manifold.

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 manifold.

Shortly, the curvature of a Riemannian manifold is a geometric quantity that measures how much the manifold curves. It can be computed from the . makes use of the concept of curvature by imposing, through the Einstein field equations, that the curvature of is determined by means of the .

1855 questions
169
votes
7 answers

Why would spacetime curvature cause gravity?

It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration.…
user1648764
  • 2,006
158
votes
27 answers

Simple check for the global shape of the Earth

I have been on a date recently, and everything went fine until the moment the girl has told me that the Earth is flat. After realizing she was not trolling me, and trying to provide her with a couple of suggestions why that may not be the case, I've…
SBF
  • 1,441
82
votes
17 answers

How exactly does curved space-time describe the force of gravity?

I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or trampoline bending under an object, which causes…
Zac
  • 923
80
votes
6 answers

Does gravity CAUSE the bending of spacetime, or IS gravity the bending of spacetime?

In reading these discussions I often see these two different definitions assumed. Yet they are very different. Which is correct: Does gravity CAUSE the bending of spacetime, or IS gravity the bending of spacetime? Or do we not know? Or is it…
foolishmuse
  • 5,016
74
votes
2 answers

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 distance. What is the result of general theory of…
Leos Ondra
  • 2,265
72
votes
17 answers

What is the simplest way to prove the Earth is round?

Assume you've come in contact with a tribe of people cut off from the rest of the world, or you've gone back in time several thousand years, or (more likely) you've got a numbskull cousin. How would you prove that the Earth is, in fact, round?
tQuarella
69
votes
6 answers

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 the given spot? I can grasp the meaning of…
Džuris
  • 3,227
61
votes
5 answers

What is really curved, spacetime, or simply the coordinate lines?

It is often said that, according to general relativity, spacetime is curved by the presence of matter/energy. But isn't it simply the coordinate lines of the coordinate system that are curved?
Bob
  • 943
  • 9
  • 14
60
votes
11 answers

Is spacetime wholly a mathematical construct and not a real thing?

Speaking of what I understood, spacetime is three dimensions of space and one of time. Now, if we look at general relativity, spacetime is generally reckoned as a 'fabric'. So my question is, whether spacetime is real or is just a mathematical…
OmG
  • 659
  • 1
  • 7
  • 15
49
votes
4 answers

What is the physical meaning of the connection and the curvature tensor?

Regarding general relativity: What is the physical meaning of the Christoffel symbol ($\Gamma^i_{\ jk}$)? What are the (preferably physical) differences between the Riemann curvature tensor ($R^i_{\ jkl}$), Ricci tensor ($R_{ij}$) and Ricci scalar…
Sklivvz
  • 13,829
47
votes
15 answers

Why does the speed of an object affect its path if gravity is warped spacetime?

I think I understand the idea of thinking about gravity not as a force pulling an object towards another object but instead a warping of space so that an object moving in a straight line ends up following a path that brings it closer to the object,…
Cormac Mulhall
  • 579
45
votes
3 answers

If spacetime is curved, how would anyone know? If anyone could tell, would that really be spacetime curving?

I never had a problem accepting that spacetime is curved as a result of matter, until I learned the LIGO experiments showed that evidently the curvature of spacetime can be measured. This, to me, is very strange. Suppose the entire universe is empty…
Devsman
  • 1,683
43
votes
6 answers

Why does a flat universe imply an infinite universe?

This article claims that because the universe appears to be flat, it must be infinite. I've heard this idea mentioned in a few other places, but they never explain the reasoning at all.
Nathan BeDell
  • 691
40
votes
3 answers

Why is spacetime curved by mass but not charge?

It is written everywhere that gravity is curvature of spacetime caused by the mass of the objects or something to the same effect. This raises a question with me: why isn't spacetime curved due to other forces or aspects of bodies? Why isn't it that…
Rijul Gupta
  • 5,589
  • 5
  • 34
  • 59
38
votes
9 answers

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 gravitationally attracted are said to roll down…
Dale
  • 6,150
1
2 3
…
99 100