# 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 [tag:calabi-yau] manifold.

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### 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 ...
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### How does “curved space” explain gravitational attraction? [duplicate]

They say that gravity is technically not a real force and that it's caused by objects traveling a straight path through curved space, and that space becomes curved by mass, giving the illusion of a ...
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### 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 ...
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### 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" ...
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### Better explanation of the common general relativity illustration (stretched sheet of fabric)

I've seen many science popularisation documentaries and read few books (obviously not being scientist myself). I am able to process and understand basic ideas behind most of these. However for general ...
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### 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 ...
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### Does a moving object curve space-time as its velocity increases?

We always hear how gravity bends space-time; why shouldn't velocity? Consider a spaceship traveling through space at a reasonable fraction of the speed of light. If this spaceship, according to ...
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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_{\ ... 3answers 7k views ### Nature of gravity: gravitons, curvature of space-time or both? General relativity tells us that what we perceive as gravity is curvature of space-time. On the other hand (as I understand it) gravity can be understood as a force between objects which are ... 14answers 125k views ### 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 ... 3answers 5k views ### 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 ... 2answers 2k views ### Bowling ball on a rubber sheet analogy - what pulls the ball down [duplicate] Possible Duplicate: Does the curvature of spacetime theory assume gravity? Since I read Cosmos long ago, I see the same analogy about the balls rolling on a rubber sheet used to explain how ... 4answers 20k views ### How energy curves spacetime? We know through General Relativity (GR) that matter curves spacetime (ST) like a "ball curves a trampoline" but then how energy curves spacetime? Is it just like matter curvature of ST? 2answers 3k views ### Why does dark energy produce positive space-time curvature? My understanding is that dark energy, or equivalently a positive cosmological constant, is accelerating the expansion of the universe and I have read that this gives empty space-time positive ... 9answers 9k 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 ... 5answers 4k views ### 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 ... 3answers 1k views ### Clarifying what metric counts as flat space In (2D) Cartesian coordinates, the Euclidean metric... $$\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$$ ...is flat space. If the diagonal elements are exchanged for other real numbers ... 1answer 2k views ### How much extra distance to an event horizon? How much extra distance would I have to travel through space to get from Earth to a stellar mass event horizon? (compared to the same point in space without a black hole) 2answers 9k views ### Visualizing gravity in 3D We've all seen the depiction of gravity bending space downwards, and so attracting objects into the dent it creates, cf. e.g. this and this Phys.SE posts. That's intuitive and makes a lot of sense, ... 2answers 523 views ### The meaning of potential in Bohm-Aharonov experiment The Bohm-Aharonov experiment involves a magnetic field inside a cylinder which is zero outside that cylinder. Nonetheless it affects the electrons moving outside the cylinder. The explanation for this ... 7answers 28k 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 ... 4answers 10k views ### How to measure the curvature of the space-time? I know G.R. change our vision of space and time as a unique surface than can bend. We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can ... 4answers 4k views ### ALL “forces” as manifestations of properties of space-time I apologize if this seems like a quack question, but I need some insights by those who know much more than me in Physics. Anyway, the gravitational "force" (not really a force) is a manifestation of ... 8answers 3k views ### Surely space-time Curvature does not explain gravity, it just describe its effects? In special relativity co-moving objects see the other's 4-velocity as being only temporal. When they move relative to each other they see the other's 4-velocity has rotated so that it points less in ... 2answers 907 views ### 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 ... 2answers 1k views ### Curved space-time VS change of coordinates in Minkowski space I'm looking for a rather intuitive explanation (or some references) of the difference between the metric of a curved space-time and the metric of non-inertial frames. Consider an inertial reference ... 1answer 1k views ### What is the curvature of an empty universe? My calculations tell me an empty universe has hyperbolic curvature. Is this correct? If it is, can anyone help me understand why this is intuitively? 8answers 3k views ### Physical meaning of non-trivial solutions of vacuum Einstein's field equations According to Einstein, the space-time is curved and the origin of the curvature is the presence of matter i.e. the presence of the energy-momentum tensor$T_{ab}$in Einstein's field equations. If our ... 2answers 579 views ### How do spatial curvature and temporal curvature differ? While looking at the metrics of different spacetimes, i came across the "Ellis wormhole", with the following metric: $$c^2d\tau^2=c^2dt^2-d\sigma^2$$ where $$d\sigma^2=d\rho^2+(\rho^2+n^2)d\Omega^2... 2answers 3k views ### What does it mean for objects to follow the curvature of space? In science documentaries that touch on general relativity, it is often said that gravitational pull isn't an actual a pull (as described by classical physics), but rather one body travelling in a ... 1answer 483 views ### Has a metric formulation of electromagnetism ever been attempted? [duplicate] I understand that electromagnetic fields carry energy, and this energy curves spacetime gravitationally. That's not my question. I'm asking if anyone has tried to formulate electromagnetism in such ... 2answers 688 views ### Is the popular explanation given for gravity in General Relativity misleading? [duplicate] In most popular explanations of General Relativity, both in print and film/television, gravity is demonstrated using an example of a 2 dimensional plane being flat, then when putting a heavy object in ... 2answers 936 views ### How much choice did Einstein have in choosing his GR equations? General relativity was summarised by Wheeler as "Spacetime tells matter how to move; Matter tells spacetime how to curve". I have a fairly good mental picture of how the first part works. However, I ... 2answers 964 views ### 5D Ricci Curvature As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper http://arxiv.org/abs/1107.5563. I was wondering if there is some special ... 5answers 6k views ### Naive visualization of space-time curvature With only a limited knowledge of general relativity, I usually explain space-time curvature (to myself and others) thus: "If you throw a ball, it will move along a parabola. Initially its vertical ... 5answers 2k views ### How does the curvature of spacetime induce gravitational attraction? I don't know how to ask this more clearly than in the title. 2answers 473 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 ... 4answers 483 views ### What makes a coordinate curved? Bear with me while I try to explain exactly what the question is. The question Can a curvature in time (and not space) cause acceleration? is imagining a coordinate system in which the curvature is ... 2answers 626 views ### What are the factors affecting the spacetime curvature? Large masses in space as stars and planets cause a curvature in the spacetime fabric. What are the factors that affect this curvature? Is it only mass? And can we conclude these factors using Tensors? 4answers 4k views ### Calculating the Riemann tensor for a 3-Sphere I have worked out all the connection symbols for the 3-sphere using calculus of variations, cf. this Phys.SE post. So to find the Riemann tensor I am trying to find all the nonzero components of: \... 2answers 2k views ### What is the geometrical interpretation of Ricci tensor? In differential geometry and general relativity space is said to be flat if the Riemann tensor R=0. If the Ricci tensor on manifold M is zero, it doesn't mean that the manifold itself is flat. So ... 1answer 947 views ### Computing Curvature via Cartan Formalism Given a metric g_{\mu \nu}, one can select an orthonormal basis \omega^{\hat{a}} such that,$$ds^2= \omega^{\hat{t}}\otimes\omega^{\hat{t}} - \omega^{\hat{x}} \otimes \omega^{\hat{x}} - ...$\$ By ...
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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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### 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...)
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### If the universe is 3D, how is space-time like a “fabric”? [duplicate]

I have been taught that space-time should be viewed as a fabric and that objects with a large gravitational influence indent that fabric. My question is, if the singularity of a black-hole punctures ...
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### 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 ...
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### 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?
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### Why do the Einstein field equations (EFE) involve the Ricci curvature tensor instead of Riemann curvature tensor?

I am just starting to learn general relativity. I don't understand why we use the Ricci curvature tensor. I thought the Riemann curvature tensor contains "more information" about the curvature. Why is ...