What is General relativity: Definition and 999 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. A

    Special and general relativity

    If I am traveling in a spaceship in a speed close to the speed of light the time will delay right? However I am in space where there is low gravity which means that time will speed up. What will exactly happens to time will it speed up because of low gravity or delay because of the speed...
  2. S

    Conservation of energy in general relativity & non-existence of PMMs

    Hi. I saw this: http://physics.stackexchange.com/questions/35431/is-the-law-of-conservation-of-energy-still-valid Now, if that's the case, then I wonder about a related question: can general relativity be used to create perpetual motion machines? If not, then why not (i.e. how does energy...
  3. N

    Are clocks used in general relativity?

    In special relativity clocks are used to record events and proper time gives the time in an inertial frame so two times are used. In general relativity I only see proper time being used. Is there an implicit understanding about clocks?
  4. Astronuc

    Relativity A First Course in General Relativity by Bernard Schutz

    Author: Bernard Schutz Title: A First Course in General Relativity Amazon Link: https://www.amazon.com/dp/0521887054/?tag=pfamazon01-20 Prerequisities: Better part of a undergraduate (BS) physics program Contents: Undergraduate, upper level; Graduate, introductory Table of Contents...
  5. Z

    General Relativity Lecture Videos

    Is there a list of all the general relativity lecture videos somewhere? Most of the videos I find do not have very good resolution of the black boards.
  6. R

    General Relativity: Prove that Four-Vector is 0

    Homework Statement Show that Ui \frac{dU^i}{d\tau} = 0 Homework Equations Raising Indices: Ui = gkiUi = Ui where gk is a dummy index The Attempt at a Solution I'm interpreting this question to mean a scalar multiplying each component of a four vector = 0. Also, since the same...
  7. N

    Rigorous definitions in general relativity

    Hello (a) The universe U is a topological space whose elements are called events and as each event has a neighborhood homeomorphic to R^4. (b) A local coordinate system is a homeomorphism between an open subset of U and a bounded subset of R. (c) A world line segment is a continuous...
  8. micromass

    Relativity A First Course in General Relativity by Schutz

    Author: Bernard Schutz Title: A First Course in General Relativity Amazon Link: https://www.amazon.com/dp/0521887054/?tag=pfamazon01-20 Prerequisities:
  9. micromass

    Relativity An Introduction to General Relativity by Hughston and Tod

    Author: L.P. Hughston and K.P. Tod Title: An Introduction to General Relativity Amazon Link: https://www.amazon.com/dp/052133943X/?tag=pfamazon01-20
  10. bcrowell

    Relativity Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carroll

    Author: Sean M. Carroll Title: Spacetime and Geometry: An Introduction to General Relativity Amazon Link: https://www.amazon.com/dp/0805387323/?tag=pfamazon01-20 Download Link: http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll_contents.html Prerequisities: Contents: Contents: 1...
  11. Greg Bernhardt

    Relativity General Relativity by Robert M. Wald

    Author: Robert M. Wald Title: General Relativity Amazon Link: https://www.amazon.com/dp/0226870332/?tag=pfamazon01-20 Prerequisities: Contents:
  12. A

    Understanding General Relativity

    Hi all, I'm having a discussion with someone who believes they understand GR, here is their understanding of how gravity works... "The time and space at your feet are different from the time and space at your head. This has been experimentally verified, especially in terms of the time...
  13. W

    Software for General Relativity

    What is the best software for GR calculations ? GRTensor ?
  14. D

    Difference between the special and general relativity

    can you explain me please the difference between the special and general relativity i did some research and only what i found and what i understand and i ' m not sure is that te SR is applied only in inertial frame and the GR is applied in the noninertial frame correct me please if i ' m...
  15. H

    What class is general relativity taught in?

    I'm in the United States, taking undergraduate courses, and I believe I had what was an introduction to special relativity in Modern Physics class (Lorenz transformations, time dilation, the relativistic doppler effect, time dilation, length contraction, etc.). I just wonder what class general...
  16. A

    What is the challenge in defining mass in general relativity?

    I have a broader question on this - is mass at all properly defined in GR context, including rest mass or so-called invariant mass? Leaving aside concept of mass gain, I have been under the impression that mass itself is defined in different ways in different situations in GR, with caveats...
  17. A

    Courses A Course Plan to Master General Relativity

    So this is purely for self-study purposes. Say I'm very keen on understanding GR well, but I don't even have the prerequisites done for even starting to grasp GR. Would anyone be able to give an outline of the skills necessary in understanding GR? An outline would look something like this...
  18. shounakbhatta

    Exact Solutions to General Relativity & Einstein's Field Eqns.

    Hello, Can anybody tell me what is meant by exact solution to General Relativity or exact solution to Einstein's field equation. -- Shounak
  19. F

    Some questions about general relativity

    Hi, I have some questions about general relativity. I'd appreciate if somebody could enlighten me :) I heard that according to Einstein, objects do not accelerate in a gravitational field, it is just spacetime that is warped around them. So what exactly does this mean? Is it that due to...
  20. S

    Black holes and General Relativity

    Hello everybody, I was watching a documentary about black holes the other day and I noticed something odd. General Relativity is said to break down when you apply the mathematics on a singularity. In this case, the center of the black hole. The radius of a singularity would be 0. Now there...
  21. S

    General Relativity: Spatial Inversion Symmetry

    I am unable to find any source describing at any lengths transformations of the type x \rightarrow -x beyond the case of static spacetime (and even in the case of static spacetime, it is rarely the fundamental definition, which tends to be more along the lign of orthogonality with an...
  22. S

    Name of general relativity symmetry

    People seem to be seriously looking for "Lorentz violating" neutrino oscillations - meaning direct violation of special relativity. What is a short name for the symmetry that distinguishes general relativity from special (the symmetry between acceleration and gravity)?
  23. 7

    Is it true that in general relativity length does not exist?

    I think I read once that length does not exist in general relativity, though I'm not sure if I got that hopelessly muddled or if there are subtleties that I am missing. I have a vague understanding of length contraction, but I thought that what I was reading said that there simply is no length...
  24. T

    General relativity - Covariant Derivative Of F(R)

    In f(R) gravity as http://en.wikipedia.org/wiki/F%28R%29_gravity , i have problem with the term [ g_ab □ - ∇_a ∇_b ] F(R) , well actually is [ ∇_b ∇_a - ∇_a ∇_b ] F(R) , but F is a function of Ricci Factor and Ricci Factor is expressed as a(t) ( scale factor ) . for the a = b = 0 i say this...
  25. C

    General Relativity gravitational redshift

    Homework Statement The gravitational redshift tends to decrease the frequency of light as it travels upwards a distance h,\frac{\Delta{f}}{f_{0}}=\frac{-gh}{c^2} integrate both sides of this equation (from the surface of the gravitation body out to infinity) to derive the expression for the...
  26. S

    Exact Solutions for General Relativity

    I would like to know if there are exact solutions using General Relativity to determine: 1) time dilation from velocity, and 2) velocity from redshift (arising from kinematic movement). I understand that Special Relativity can handle both of these questions, but the implementation of SR is...
  27. C

    Basic questions about General Relativity

    I know little to nothing about G.R. but it is interesting to look up knowledge,especially physics, so please correct me if I am wrong.. It is easy to picture how one giant mass distorts spacetime on 2D scale, but what if there is multiple bodies of masses present and would this turn into a...
  28. F

    General relativity: Rindler space problems

    Homework Statement I have derived the metric in for 2D Rindler space in a previous problem and it is explicitly given again here: ds^2 = dx^2 - (dx^0)^2 = dw^2 - (1+gw/c^2)^2(dw^0)^2 , where (x^0, x) are Minkowski coordinates in an intertial system I and (w^0,w) the Rindler coordinates of a...
  29. marcus

    Lifting General Relativity to Observer Space

    On 2 October, 5 days from now, Derek Wise will give an online international seminar talk which will be a followup to his June 2012 paper with Stefen Gielen---as I recall a lot of us found that paper very interesting and it topped the second quarter MIP poll. So I want to review that paper, the...
  30. CJ2116

    Topology and Differential Geometry texts for General Relativity

    Hi everyone, I was wondering if I could some advice from anyone who has some experience with higher level general relativity. Any help would be greatly appreciated! Some background: I'm currently working through Robert Wald's General Relativity and am struggling a lot with the "advanced...
  31. A

    General relativity and tidal forces

    Tides on Earth are described with Newton's theory of gravitation. Relativistic effects on tides theoretically become measurable on very strong gravitational fields, possibly becoming twice as strong as tides predicted by Newtonian gravity: http://adsabs.harvard.edu/abs/1983ApJ...264..620N...
  32. K

    Experimental Physicist: Is Learning General Relativity Necessary?

    Hi, I am in my 3rd year and have General Relativity as one of my options. I'm kind of feeling the peer pressure of selecting General Relativity, but putting all the hype aside, is it really necessary to learn General Relativity for an Experimental Physicist? I have to say, maths isn't really...
  33. CJ2116

    Question about theorem 2.2.1 in Wald's General Relativity

    Hi everyone, first of all I have been a lurker here for years and have benefited greatly from many of the discussions in the math and physics sections. Thanks, I have received a lot of helpful information from these forums! I have been working through Wald's General Relativity book and I am...
  34. G

    Time reversal in General Relativity, and black holes

    Plain old Newtonian mechanics is time-reversal invariant, i.e. if you view a recording of some events played backwards, it would still appear to be following the same physical laws (gravity attraction law in particular). This type of "time reversal" is exactly equivalent to just turning every...
  35. L

    Visualizing General Relativity with Fluid Analogy

    I'm interested in using a fluid analogy of general relativity to more easily visual what is going on in certain situations, without having to resort to visualizing curved 4d space time which is doesn't come to naturally. However, I don't know relativity quite well enough to understand what...
  36. S

    Monkey and Hunter Problem - General Relativity?

    Hi You guys probably have heard about the monkey and hunter problem. Basically in the monkey an hunter problem you can see the dart hits all the time if you observe the experiment in an accelerated frame of reference ie your falling with the monkey. You see the bullet travel in a straight...
  37. D

    Foundations of General Relativity Text - Recommendations

    I'm looking for a good text on the foundations of GR. Geared towards physicists, but with a focus on the subtleties of the ideas that went into building the theory rather than on applications. Any recommendations? Thanks!
  38. V

    General Relativity Equations

    Homework Statement Essentially, my adviser just told me to get the equation, then expand it so that it doesn't have any tensors. That's it. Just get rid of the tensors. He said that this would be normally found in some textbook...? I've searched a lot of books, but I never saw anything...
  39. B

    Measured lightspeed in general relativity and moving through space.

    Hey guys I was just wondering the following. Since time slows down when traveling faster, and we move around 1.3 million miles per hour, using the CMBR as a frame of reference. Does this mean our perceived lightspeed is wrong? How fast would we measure time to travel if we managed to come to...
  40. E

    [General Relativity] Find the acceleration of an object

    Homework Statement Given the metric ds^2=-e^{2\phi}dt^2+\frac{1}{1-\frac{b(r)}{r}}dr^2 find the time component of the 4-acceleration of an object moving with velocity v in the r direction.The Attempt at a Solution The four-velocity of the object is u^a=(t', v) where the prime stands for the...
  41. A

    General relativity for a master degree?

    What aspects of general relativity one could study for a master degree?
  42. soothsayer

    General Relativity vs. quantum gravity

    Hey all! So, in my study of general relativity, I've come to understand that gravity is actually what physicists would have classically called a "fictitious force", in that it is a force derived from the fact that the observer is not in an inertial reference frame, like in the case of the...
  43. D

    Higgs field and General Relativity

    If the Higgs field is responsible for embuing particles with mass, and mass is responsible for gravity, is it possible that the Higgs field will provide the missing link between general relativity and quantum mechanics ie could the Higgs field be the basis of a quantum theory of gravity?
  44. Orion1

    Alcubierre metric and General Relativity

    Alcubierre metric: ds^2 = \left( v_s(t)^2 f(r_s(t))^2 -1 \right) \; dt^2 - 2v_s(t)f(r_s(t)) \; dx \; dt + dx^2 + dy^2 + dz^2 What formal conditions are required to verify a valid metric solution of the Einstein field equations? How many possible valid metric solutions are there in General...
  45. S

    Proper Time in Special vs. General Relativity

    We know that the proper time between two events is the shortest possible time between those two events that can be measured in any frame. This follows from the idea that moving clocks run slow-- a stationary clock at rest in S' which moves relative to S at a constant speed v will be time dilated...
  46. A

    How dominant is gravity stated in general relativity.?

    Is gravity strong enough to attract 2 galaxies togeather in Gr..I mean is gravity present everywhere in the universe or are there places in universe filled with vacuum and has no gravity waves through it.?
  47. I

    Tensor calculus for general relativity question.

    Use the metic that Einstein proposed in the first cosmological model based on general relativity. ds2 = -dt2 + (dr2) / (1 - Kr2) + r2(dθ2 + sin2θd\phi2) where K > 0 Show that the stress energy tensor is that of a static, spatially uniform perfect fluid and determine ρ and p in terms of G and...
  48. johann1301

    Length contraction and general relativity

    Can one detect length contraction due to general relativity? I.e does length/width/height change with distance to a gravitational centre? If so does the object get longer or shorter? I know this is the case with increasing speed in special relativity, but what about GR... If i went into...
  49. A

    Is there a more beginner-friendly book to learn General Relativity?

    I'm not sure if this is the right place to post this topic, but I need some opinions. I would really love to learn General Relativity. I possesses a working knowledge of tensors (namely tensor calculus and analysis). Upon doing some research I was told Gravitation by Misner, Thorne, and...
  50. tom.stoer

    Two-body problem in general relativity

    Suppose we have two bodies of equal mass m and with hyperbolic motion and with small, fixed impact parameter. Now let's assume the speed of the two bodies in the c.o.m frame approaches c. Is there a way - with a delta-function ansatz for the energy-momentum 4-tensor - to understand the...
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