Spacetime curvature Definition and 88 Threads

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. I

    Exploring Spacetime Curvature and Light

    Hi, So according to GR, energy bends spacetime, right? So that would include both light and mass. If I am understanding this right, light bends spacetime, and is also affected by the spacetime curvature. Could someone explain exactly what the spacetime curvature does to light (I mean like how...
  2. J

    Spacetime Curvature: Which Tensor Gives Coordinates?

    In the Einstein Field Equations: Rμν - 1/2gμνR + Λgμν = 8πG/c^4 × Tμν, which tensor will describe the coordinates for the curvature of spacetime? The equations above describe the curvature of spacetime as it relates to mass and energy, but if I were to want to graph the curvature of spacetime...
  3. Atlas3

    Does light receive a spacetime curvature upon refraction?

    could the bend be described mathematically? Not the vector the curvature.
  4. newjerseyrunner

    If space is curved, could it be detected

    I was contemplating the size and shape of the universe. Our observable universe is perfectly 3D spherical, but that's a result of a finite speed of light and a beginning of time, and I was wondering if there was a way to deduce the size of the universe. I imagined the universe as a 4D sphere...
  5. 5

    Realizing Warp Drive with Matter-Antimatter Fuel Cells

    My question is related to M. Alcubierres paper on the warp drive within general relativity. I was wondering about the realizability of this, setting the three energy conditions aside for the moment. Assuming the highest energy density known to me as an energy source, namely something like...
  6. Leonardo Muzzi

    How are tidal effects explained by general relativity?

    I can fairly understand the concept of gravity as a curvature in space time in general relativity, but so far I could not understand completely the tidal forces explained by the curvature of spacetime. When the moon is on one side of the earth, the oceans on this side come closer to the moon...
  7. DiracPool

    3-d versus 4-d spacetime curvature

    A second SR question that has been on my mind lately is that of hyperbolic nature of Minkowski space. The fact that the invariant interval, or lines of constant delta S trace out a hyperbola according to the equation, ##x^2-(ct)^2=S^2##, is fascinating to me and seems to imply that space-time...
  8. HowardHughes

    Imagining spacetime curvature more accurately

    I am intrigued to see what spacetime curvature is like in reality. Most images or ways to imagine it tend to look at spacetime as a fabric which it is not precisely. So how would be best to imagine it... Do any of the picture demonstrate this? What is the best way to imagine it?
  9. S

    Science fictiony questions about spacetime curvature

    I'm writing a sci-fi story and I'd like to make it, at the very least, scientifically plausible (in the way that alcubirre warp drives are possible assuming we could get our hands on something with negative mass which, as far as we know, doesn't exist). The basic assumption for these questions...
  10. 4

    Is there always the same amount of spacetime curvature in the uni.?

    Is there always the same "amount" of spacetime curvature in the uni.? Universe is what I meant by uni. Okay, if matter and energy cannot be created or destroyed, and since they are what causes spacetime to curve, does that mean there will always be the same amount of spacetime curvature...
  11. S

    Question about spacetime curvature

    This maybe a simple question, but if Earth orbits the Sun due to the Sun's mass 'curving' spacetime, wouldn't we be moving closer to the sun? like if you spun a marble around within a bowl, it ends up in the center. What am I missing here?
  12. P

    Evidence of Electromagnetic fields causing spacetime curvature?

    Hi All, Just wanted to know, is there any experimental or observational evidence today, that electromagnetic fields can cause spacetime curvature? Either direct or indirect?
  13. V

    Thought experiment involving spacetime curvature:

    Peter Donis and Nugatory taught me a lot about spacetime curvature yesterday, but it has left me with so many questions. It sounds like mass slows down time as it warps spacetime. So, I suppose this means: more mass = more spacetime curvature = less time elapsing. Okay, in addition to...
  14. T

    Relative acceleration of geodesics and spacetime curvature

    Mass curves spacetime. The relative acceleration of nearby geodesics of free test particles indicates the sign of the spacetime curvature. Convergent geodesics mean positive, divergent negative curvature. But also the metric expansion of space curves spacetime. The geodesics may be convergent...
  15. X

    Gravity question: force vs spacetime curvature

    So Newton says that gravity is an attractive force and some people believe in gravitons to transmit that attractive force, but Einstein says the attraction is actually due to moving along the curvature of spacetime (caused by the bodies' mass). I'm not asking which is correct, but my question is...
  16. R

    Does Higgs Boson rule out spacetime curvature?

    Hi there: I've learned that there's no such thing as gravity, just the curvature of spacetime that makes objects that are close to each other act like it existed. Does Higgs Bossom discovery tell us that there is a gravity force after all?
  17. P

    Spacetime curvature observer and/or coordinate dependent?

    Spacetime curvature observer and/or coordinate dependent? In another topic several people suggested that spacetime curvature is not absolute, it apparently depends on the observer and/or coordinate system. Apparently if someone goes fast (whatever that might mean in relativity) curvature is...
  18. T

    Spacetime curvature and the force pulling an object down the curvature

    Spacetime curvature and the force pulling an object "down" the curvature ok , I have a question about the current model of gravity. If mass bends spacetime I understand that it accounts for things like how long light takes to travel through its geodesics but "why" does this curvature make...
  19. zonde

    Backreaction of accelerated motion on spacetime curvature

    Curvature of spacetime tells us how the body is moving when it moves inertially. But if the body is not moving inertially does it causes backreaction by affecting spacetime curvature? Say if we compare body that is in free fall toward planet with body that is at rest on the surface of planet.
  20. T

    Exploring Spacetime Curvature: The Role of Mass and Gravitational Force

    1) Is it always a given that the spacetime curvature will be flat in a region in which there is no mass? 2) Therefore is the curvature directly dependent on the mass in a particular region? 3) Also, what exactly is included in the term "mass"? 4) If there are no matter fields to curve...
  21. W

    Trying to understand spacetime curvature

    I'm familiar with space and time together being 4 dimensions and that mass causes a curvature in this spacetime. When I consider a line that is curved, I can view the curvature because the line is drawn on a 2D surface (plane). So, it seems an additional dimension is required for a...
  22. D

    Is Spacetime Curvature Real? - Take 2

    Alright, my first thread with this title got locked down. Let's see how long this one lasts ;-) Actually, this time I have a specific queston. It is often stated there is no test that can determine if space time curvature is truly real. What about LIGO? As I understand it, with the...
  23. D

    Spacetime curvature: Real or Not?

    Hi, I'm new to this forum so maybe this topic has been addressed ad nauseum at some point before, so I apologize if so. But, as the title suggests, do you feel the spacetime curvature is a reality, or is it just a mathematical convenience for making predictions? dm4b
  24. S

    Spacetime Curvature: Exploring General Relativity

    General relativity has it that the spacetime continuum is curved. The physics of continuum is dealt with [stress] tensors. My questions: (1) The presence of a mass creates the curvature in spacetime. By how? (2) If the curvature due to matter is positive, is the curvature due to antimatter...
  25. H

    .Exploring Spacetime Curvature to General Relativity

    I was just gong to learn general relativity(not with maths) but with some very basic tutorials given over internet. I also watched the animated series of general realtivity. Everywhere i see,matter bends spacetime( a fabric of spac and time woven ). And when there is matter than this...
  26. e2m2a

    Does energy alone contribute to spacetime curvature?

    Do Einstein's field equations explicitly show that energy alone can curve the metric of spacetime? True, energy is included in the stress-energy tensor, but is it assumed that energy in of itself curves spacetime? Or, is it possible that only energy "embedded" in mass contributes to...
  27. A

    Where does all this spacetime curvature come from?

    Hi, From what I know, science is the study of the observable world, its theories are supported by evidence. Now GR is a theory, and it informs that mass curves the 'fabric' of space and time. The thing I don't understand is that there is no evidence of mass curving spacetime, then how is...
  28. M

    Gravity from spacetime curvature

    After a while of trying to understand this, it's still kind of confusing. I get how the planets orbit around the sun because of the sun's spacetime curve, but if one were to drop something, how does spacetime curvature cause it to fall? How can everything in the universe have a gravitational...
  29. L

    Spacetime Curvature: Matter & Metric Influence Explained

    in this article http://en.wikipedia.org/wiki/General_relativity it says in the first paragraph that the curvature of spacetime is related to the stress energy tensor i.e. the matter in the universe. i.e. the curvature at a particular point depends on the matter present at that point...
  30. S

    Does spacetime curvature of EM field affect zero-charge particles?

    I've read in a few places that the energy and momentum of the electromagnetic field will itself induce a curvature of spacetime, much like the presence of matter. I'm not very familiar with general relativity, but does this imply that particles with mass and zero charge will still be affected...
  31. N

    Electromagnetic spacetime curvature effects

    In a nearby thread: I believe it was correctly concluded "yes" because an electromagnetic (EM) field has energy and pressure so it curves spacetime; it does have a gravitational effect. Although it was not discussed, this effect is much, much smaller than the electromagnetic effects because...
  32. A

    Physical interpretation of spacetime curvature?

    Folks, I'm in the process of trying to understand spacetime curvature in general relativity. My question might sound odd, but I'm wondering how to best conceptualize spacetime distortions due to a moving mass. If there is a large mass, e.g. a planet, moving through spacetime, the curvature...
  33. P

    What is the cause of spacetime curvature?

    hey folks, as far as I understand, according to Einstein's general theory of relativity, any mass that exists in spacetime causes a curvature in it, right?! now, my question is: does this curve take place in the time dimension (ct) or in spacetime (ct,x,y,z) itself?
  34. PhanthomJay

    Does Spacetime Curve Into Hidden Dimensions? Understanding Curvature

    That famous experiment during a solar eclipse, which showed the curvature of light from a star as the light rays passed by the sun, pretty much I gather confirmed Einstein's space time curvature theory. Question: Does spacetime curve into one of those hidden spatial dimensions that M-theory...
  35. J

    Understanding Spacetime Curvature: Exploring the Effects on Matter/Energy

    This may be a simple question for some of you but it has baffled me for a long time. When we say that spacetime is curved, do we mean that from a flat space of a higher dimension, our spacetime would appear curved, in the same way that the surface of a sphere looks curved when viewed from...
  36. L

    Spacetime Curvature: Exploring Stephen Hawking's The Universe in a Nutshell

    I am reading The Universe in a Nutshell by Stephen Hawking, a book everyone here has probably read, or at least heard of. In the first chapter, he talks about how the effects of acceleration and gravity prove the curvature of spacetime. I'll give you some exact quotes from the book to make it...
  37. W

    How gravity arises from spacetime curvature?

    Hi there I've been trying to find out how spacetime curvature actually produce gravity, but all i can find is articles using math, which is far too advanced for me to understand. Can anyone give me a theoretical explanation to how the gravity arise from the spacetime curvature according to...
  38. Antonio Lao

    Can Spacetime Curvature change c ?

    I am not sure.
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