What is Space-time curvature: Definition and 34 Discussions

General relativity, also known as the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the gravitational time delay and singularities/black holes. The predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. Unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity; and how gravity can be unified with the three non-gravitational forces—strong, weak, and electromagnetic forces.
Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes. For example, microquasars and active galactic nuclei result from the presence of stellar black holes and supermassive black holes, respectively. The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration LIGO. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.
Widely acknowledged as a theory of extraordinary beauty, general relativity has often been described as the most beautiful of all existing physical theories.

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  1. steve1763

    A Determining Geometry of Line Element: A General Method?

    Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how does one determine the shape of the space? Thanks
  2. N

    I Space-time curvature and the fabric of space

    Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the...
  3. M

    I Uniform gravity's space-time curvature

    In an ideal world with uniform gravity field, what does its space-time curvature look like? Is it non-zero? If not, how a free particle would be accelerated with the point view of space-time curvature? By uniform gravity field, I mean a gravity field with same value, same direction everywhere...
  4. gaaah

    B Gravity Illusion: Questions on Space-Time Curvature Granularity

    I wonder if someone would field a beginner's muse I had: If gravity is just an illusion of the curvature of space caused by mass, does not the matter within that space follow the curve? and what is the granularity of that curvature? Does the curvature exist in the space between the nucleus and...
  5. A

    A Gravity as space-time curvature?

    Hi there. I was wondering that if mini or micro black holes could theoretically exist, and if not all black holes need to "devour' matter, then could it be possible that all things we perceive to have gravity could possibly be caused by a mini or micro black hole at the center of massive objects...
  6. M

    I Mass Curving Space-Time: Equations Explained

    It is often said that gravity is a curvature of space-time and not a force. But since gravity is caused by mass, there must be some way in which mass curves space-time. What are the equations for how mass affect space-time?
  7. P

    B General Relativity and Gravity?

    We recently touched base with gravity in regards to general relativity and I'm a bit perplexed. So apparently (and correct me if I'm wrong) gravity is created when the mass of the universe warps, or bends, space-time. I've read all those analogies about a trampoline curving due to an object of...
  8. lynchmob72

    How does space-time curvature affect light?

    If space is warped around heavy objects in space, i feel that space would be FUBAR around black holes. So, my question is, Does light get sucked in by gravity, or does it just get caught in the warped space around a black hole?
  9. K

    Space-Time Curvature in General Relativity

    Suppose we are in a Minkowskian space, away from all the source of gravity, and observe an accelerated frame from this frame. Acoording to Equivalence principle, we can consider the accelerated frame to be at rest and assume we have gravity in the accelerated frame. Thus, observer in the...
  10. S

    Inverse curvature of space-time

    Assuming that my understanding is correct, I believe it was Einstein who proposed that gravity is the result of the warping or curving of space-time. My question is this: if gravity, which is solely attractive in nature, is the result of warped or curved space time, then is it possible for the...
  11. T

    Light Speed Photon: Everywhere at Once?

    A photon traveling from its source at light speed is said to not experience time and therefore be everywhere at once. Well not exactly, it can only be everywhere at once along its projected path assuming the photon's path in a vacuum is not altered by anything. Time itself cannot alter the...
  12. T

    Quantum Tunneling: Can Photons Escape Black Holes?

    Could a photon utilize quantum tunneling to escape the threshold of a black hole or the confines of the curvature of space-time? Could any particle for that matter?
  13. J

    Dark Matter. Space-Time curvature. Galaxy formation

    1. Gravity is the geometric curvature of space-time caused by massive objects. 2. Dark Matter surrounds galaxies. 3. Dark Matter is thought to be critical in galaxy formation. 4. The mass of Dark Matter creates curvatures in space-time around baryonic matter which forms galaxies. What roles...
  14. Drakkith

    Types" of Space-Time Curvature in GR

    When we talk about space-time curvature or the curvature of space, how many different "types" of curvature are there according to GR? For example, the rounded surface of a cylinder is curved in only 1 dimension, while the other is flat. For a sphere, both dimensions of the surface are curved...
  15. K

    Space-time curvature without mass-energy ?

    Hi everybody, As you know, the Einstein field equation R_{μ\nu} - 1/2Rg_{μ\nu} =κT_{μ\nu} implies that at any point with vanishing energy-momentum tensor the Ricci curvature also vanishes: T_{μ\nu} = 0 \Rightarrow R_{μ\nu} = 0 hence a Ricci-flat space-time (the vacuum...
  16. P

    Single equation for space-time curvature?

    Is there a single equation that can model both spatial and temporal metric contraction simultaneously? And also what's that equation that can model the actual degree of curvature n space-time that uses trig functions and how do you use that in combination with the two previously mentioned...
  17. E

    Space-time curvature as gravity only for speeding particles?

    If gravity rises from the fact that mass bends space-time and stuff falls in because it actually follows a straight line in a curved space as it moves by a gravitating object - doesn't that mean that a relatively stationary particle would not fall in the the claws of gravity as it would NOT be...
  18. G

    Space-Time Curvature Question

    Space-Time Curvature Question! Hi Guys, A question about the curvture of space-time by mass. Where is the point of maximum curvature?? Is it at the centre of mass (i.e.. the middle of the body) The reason I ask, is that when space-time curvature is shown visually it makes out like it is a...
  19. K

    Gravity as space-time curvature and the need to unify it with quantum mechanics

    Hi there. This is my first posting to this forum, and in fact to any forum in many years, so please excuse me if I have not followed the rules correctly or chosen the correct forum. I have been watching a lot of Neil DeGrasse Tyson-related videos and it has lead me to a line of thinking...
  20. G

    Space-Time Curvature: A New Perspective on Dark Matter?

    Could it be possible that space-time curvature is not caused by matter but is an inherent characteristic of space-time? Wouldn't this explain dark matter?
  21. M

    Space-Time curvature? the units?

    What would the units be on the curvature of spacetime? G(curvature)=8πGT/c^4
  22. jfy4

    Phase, Geodesics, and Space-Time Curvature

    Please read and critique this argument for me please, any help is appreciated. Imagine a geodesic, and a matter wave that traverses this geodesic. The action of this matter wave determines the motion of the matter wave along this geodesic over a given space-time interval, and is specified...
  23. jfy4

    Phase, Geodesics, and Space-Time Curvature

    Please read and critique this argument for me please, any help is appreciated. Imagine a geodesic, and a matter wave that traverses this geodesic. The action of this matter wave determines the motion of the matter wave along this geodesic over a given space-time interval, and is specified...
  24. M

    'Direction' of space-time curvature ?

    Hi, I'm new here. I want post a specific question that's been rattling around in my head. Basically, if you consider the curvature of 3 dimensional space into a 4'th dimension due to gravitational field, has anyone considered the 'direction' of that curvature ? If you think about the...
  25. K

    Are space-time curvature 3D

    General Relativity explains that every single piece of mass alters the space-time fabric, creating a curve. But since we live on a three-dimensional universe shouldn't the curvature alter the fabric in every dimension, creating some kind of weird closed curve that might look as a bubble around...
  26. T

    Is there a Space-Time Curvature equation?

    I've been wondering if there is a relationship between the mass of an object and how much it "curves" space-time. I can't seem to find an equation or connection, I have looked at four-momentum but am not certain what it actually calculates. Maybe I just don't know it and there is yet an equation...
  27. N

    Gravity: force or space-time curvature?

    Please note that I do NOT want to discuss whether gravity is a force or the effect of space-time curvature here. If you want to discuss this, please post a separate topic about it. What I wanted to ask is what Einstein's own beliefs on this were. Up till now I had always believed he had...
  28. C

    Maximum space-time curvature?

    First I thought If nothing can move faster than c, then nothing can accelerate faster than c/sec, right? Well, that means that the maximum amount space-time can curve is up to the ol' 45 degree slope, not like straight down as some black-hole pictures are made. Right? And then I thought...
  29. C

    Motion in space due to space-time curvature

    Why do things orbiting, i.e. free-falling, around Earth float away from each other? Why don't they both free fall toward Earth together? I remeber hearing once that if you let go of 2 objects while 'floating' in space they both go away from you and away from each other. Is this due to curving...
  30. redtree

    Relativistic mass and space-time curvature

    Does relativistic mass curve space-time, i.e., does relativistic mass affect the gravitational field of an object?
  31. U

    Can space-time curvature be applied to artificial satellites.

    I do wonder if space-time curvature can be applied to artificial satellites ... I think yes because that could be the reason why they are revolving around earth. Doubt:But what happens if they gain velocity more than the escape velocity. I could be conceptually wrong but if the above...
  32. M

    Space-Time Curvature in General Relativity

    Is it accurate to claim that space-time curvature in general relativity means a curvature of a space-time with a Minkowski pseudo-metric?
  33. D

    Does anybody have a better analogy of describing space-time curvature?

    The old 2D paper describing 3D curvature is a little lame because it uses gravity to describe gravity. You know, the little ball circling the 2D psuedo-black hole, well remove gravity and the ball would fly off the 2D paper, you can't use gravity to describe gravity. It would be like saying...
  34. F

    Space-Time Curvature: Causes & Movement

    I understand that the curvature is caused by the depression of a mass in the space-time surface. What I don't understand is what is causing this depression. For example, is it the bodie's resistance to the motion of the space-time surface? Or is it that the curvature is caused by the...