Curved space Definition and 82 Threads

Curved space often refers to a spatial geometry which is not "flat", where a flat space is described by Euclidean geometry. Curved spaces can generally be described by Riemannian geometry though some simple cases can be described in other ways. Curved spaces play an essential role in general relativity, where gravity is often visualized as curved space. The Friedmann-Lemaître-Robertson-Walker metric is a curved metric which forms the current foundation for the description of the expansion of space and shape of the universe.

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  1. N

    Acceleration and Curvature: Understanding the Relationship

    From another thread: (Bob for short's reply) I thought acceleration DID curve space... I'm coming from this perspective: say in the rotating "rigid" disc...and via Einstein's equivalence principle... for example, Brian Greene in THE ELEGANT UNIVERSE says: any clarifications...
  2. M

    Distinguishing Curved Space vs. Coordinate Choices in Mathematics

    How do we distinguish (mathematically) between curved space and the choice of coordinates? For example, the flat space metric in spherical polar coordinates looks as if it is curved space. I can ask the same for gravitational waves - how do we know that it isn't the TT gauge which is wavelike...
  3. S

    What Do I Observe Moving Around in Curved Space

    I understand some of the basic concepts of curved space, flat, positive, negative, spheres, saddles, etc. In flat space, if one measures the angles of a triangle, the sum adds to 180 degrees. In spherical space, the sum is greater than 180. OK, how do things work in spherical space? If I...
  4. W

    Equivalence Principal, Acceleration, Curved Space

    According to the Equivalence Principal, the effects of Gravity are locally indistinguishable from those of Acceleration. QUESTION: Since Gravity curves Space, a la the Flamm Paraboloid, does acceleration do the same ? Acceleration does impose a comparable Time Dilation effect, from the...
  5. B

    Raising indices in curved space

    In curved space, can I raise an index on a tensor that is being differentiated? Ie, is the following true? g^{\mu\lambda}\partial^\nu(F_{\mu\nu})=\partial^\nu(F^\lambda_\nu)
  6. D

    Can someone explain curved space time?

    I have become very interested in physics and astronomy recently and have started dabbling. I have been reading about curved space time and its association with gravity. I've also been reading about time as it is related to travel at the speed of light. Can anyone explain the concept of...
  7. L

    The meaning of time in curved space quantization

    in diffeomorphism invariant theory, which is the meaning of the time in quantization? or in other words which is the right time for quantization?
  8. R

    How to Calculate the Metric and Christoffel Symbols for GR Flat and Curved Space

    1.a) Concider the 2-space consisting of a spherical shell at constan radius, r. In polar coordinates the line element on the surface can be written (a, b,∈ 1,2) Homework Equations ds2=gabdxadxb=r2dθ2+sin2θdφ2 calculate gab, Γabc, R1212, R2121, R11, R22, R The Attempt at a Solution...
  9. D

    What Does Curved Space Really Look Like? A Visual Guide to General Relativity

    It is just something i can't get my head around, how to picture how space is curved around large masses. Is space like uniform jelly with it being denser around the planets, or is it like a void where curvature flattens out the farther away from the gravity source. Id like to hear your...
  10. F

    To transform from flat to curved space

    Many of the formulas of physics assume a background of flat spacetime. But it's natural to think that this is just a special case of a more general formulation in curved spacetimes. So I'd like to develop a general procedure to transform flat space formulas and integrals, etc, into their curved...
  11. N

    Find Area of Curved Space | 2D, Positive Geometry

    [SOLVED] Area of curved space Homework Statement I have the following metric, which describes a 2D, positive curved space with flat geometry (ie. a sphere): ds^2\,=\,dr^2\,+\,R^2 \sin ^2 (r/R)d\theta ^2 Here ds is the distance between two points (r, theta) and (r + dr...
  12. N

    Prove: Sum of angles > 180 in curved space

    [SOLVED] Prove: Sum of angles > 180 in curved space Homework Statement If I have a positively curved space (i.e. a sphere) and I draw a triangle on it, the sum of the angles of the triangle exceed \pi, more precisely, v1 + v2 + v3 = pi + A/R^2 where v1, v2 and v3 are the angles of...
  13. N

    Topology of Curved Space: Understanding Distance on a Positively Curved Sphere

    [SOLVED] Topology of curved space Homework Statement The distance between a point (r, theta) and a nearby point (r + dr, theta + d\theta) on a positively curved sphere is given by ds^2 = dr^2 + R^2 \sin ^2 (r/R)d\theta ^2 NOTE: I mean that ds^2 = (ds^2). My question is - how do I...
  14. C

    Questions about gravity and curved space

    Hi, i just found this forum when trying to find an answer to a question. I am not a physicist, not even close, I'm in high school still. Anyway, i will try to explain my question the best i can. It would be a lot easier if i could draw it but alas i can not... I am trying to conceptualize...
  15. A

    Why do balls follow curved paths in Earth's gravity according to GR?

    The GR equ. tells us that a test particle will follow a geodesic line in spacetime, which is not a geodesic line in space. Usually space is flat, but that does not imply the geodesic line of a test particle in space is a straight line (right?). Since if I throw a ball the gravity of Earth makes...
  16. F

    Convert flat space function to curved space function?

    Is there a general procedure to convert or transform a function that is defined on a flat space into an equivalent function in curves spaces?
  17. R

    Exploring the Curvature of Space-Time in Relation to Black Holes

    JesseM wrote Light doesn't need to have mass to be affected by a black hole, since in general relativity you can explain the motion of light in terms of the the black hole curving spacetime, and light following a geodesic path in this curved spacetime. I replied as matter is...
  18. L

    Geodesics in Modified Euclidean Spaces: Is There a General Statement?

    Hi there: i have a question on geodesics in a Eculidean space equipped with a metric tensor \lambda(x)*I, where I is the identity matrix. Is any general statement that can be made towards the geodesic between two points in this modified space? My feel is that this space is quite special...
  19. jal

    Black hole entropy, curved space and monsters

    http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.3239v1.pdf Black hole entropy, curved space and monsters Stephen D. H. Hsu and David Reeb 21 June 2007 Almost all of the entropy of a given black hole must result from a smaller black hole which has absorbed some additional mass. It is also...
  20. C

    Does Pi Change in Curved Space Geometry?

    If i have a volleyball and draw a circle around the centre, then draw a line between the top of the ball and the centre and measure the two line I find that the ratio circumference of the circle to diameter of the circles is 4, thus implying that in this case pi is 4, however if I drew a circle...
  21. R

    Exploring Curved Space and Gravity: Understanding the Geodesic Line in Spacetime

    The GR equ. tells us that a test particle will follow a geodesic line in spacetime, which is not a geodesic line in space. Usually space is flat, but that does not imply the geodesic line of a test particle in space is a straight line (right?). Since if I throw a ball the gravity of Earth makes...
  22. -Job-

    Exploring Maximum Gravity: A Model to Understand Curved Space

    In trying to understand why matter curves space i thought up a model that has the curiosity of suggesting the concept of maximum gravity, suggesting that as the mass of an object increases gravity increases as well, until the mass reaches a point at which the gravity starts to increase more...
  23. L

    Could any curved space be a cut in a higher-dimensional flat space ?

    For a beginner (as I am since a long time), it is convenient to conceptualize curved spaces as embedded within a familar flat space with more dimensions. Of course the intrinsic point of view is more elegant and suffice to itself. Nevertheles, I am asking this question: are there some curved...
  24. A

    Exploring the Mysteries of Black Holes and Curved Space

    I want to start a discussion about black holes and curved space. From what i know (not including that article posted in another thread) black holes are created when stars can no longer burn and compress so much that it creates a gravitational pull that is so big even its own light can't evade...
  25. G

    Parabolic PDE in Curved Spaces: Exploring Solutions on Manifolds

    The parabolic approximation was introduced by Leontovich and Fock in 1946 to describe the propagation of the electromagnetic waves in the Earth atmosphera (see Levy M. Parabolic equation methods for electromagnetic wave propagation, 2000). However, the parabolic equation was known long before...
  26. G

    Understanding Gravity: The Curvature of Space-Time and Kinetic Energy

    I have some question that might be hard for me to phrase clearly, but I'm going to give it a try. So, as far as I understand it, according to GR gravity is a side effect of the way mass (or mass energy, or whatever) curves space-time. So that when an object "falls" to the Earth, it isn't...
  27. G

    Losing mass, gravity, curved space, and more

    I have sort of a vague question. Am I right in saying that only mass and not energy cause space to curve and have gravitational effects (and other affects that only depend on mass)? Or does the "relativistic mass" of a photon cause similar but reduced effects? That's sort of just a lead in...
  28. R

    Hovering in gravity makes curved space flat?

    Have I got it right this time? Red-shifting is determined by the difference between the space-time curvature at the light source and the observer's space-time curvature. For the light source, all that matters is the distance from the center of gravity -- I think the motion of the source...
  29. M

    Mass and Curved Space: A Question

    if mass curves the space around it is mass perhaps curved space itself?
  30. D

    Mass and Curved Space Question

    According to General Relativity, the presence of mass curves space, and this curvature causes the effects of "gravity". Do Einstein's equations give us a clue as to the mechanism by which mass is able to do this? In other words, how does mass curve space? How does it "know" to curve space? And...
  31. V

    Gravity caused by curved space - am I right?

    gravity caused by curved spacetime - am I right? I went over this with someone here a while ago and I think they became exhausted with me. Anyway, I went away to think about it. Here is what I have so far. I was told that gravity is caused by warped space time (according to, is it GR or...
  32. H

    Why Study Curved Space? Exploring the Assumptions and Realities of the Universe

    One of the things Astronomers get flak for is presuming that the universe is curved (or more precisely, their model permits the universe to curve). People think astronomers are losing touch by using these horribly abstract mathematical ideas that obviously can have no connection to physical...
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