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.

View More On Wikipedia.org
  1. Doctor Strange

    I Can Time be Measured Absolutely w/ SNe Ia Near a Black Hole?

    If I take a spaceship and park it near the event horizon of a black hole and then measure the age of the universe by observing SNe Ia, then travel back out to normal space (no gravitational forces, at rest with respect to CMB), will the dates agree? That is, if the measured age of the universe...
  2. J

    I On the invariant speed of light being the upper speed limit

    Hello! I have a question that has been bothering me since I first started learning about Special Relativity: Given only the Minskowskian metric and/OR the spacetime interval, how can one reach the conclusion that the speed of light is invariant for every observer and how can one conclude that it...
  3. S

    Relativity Introduction to general relativity

    Hello! What book should I use as an introduction to General Relativity? Something that includes an introduction of the math behind GR (tensors for example) would be much appreciated. Thank you!
  4. Meerio

    I By what formula is this graph predicted? Cumulative Periastron Time Shift

    I'm confused about how the predictions of this graph were formed. I have this formula: But the change in frequency per second is about : 2x 10^-12 which has a problem because when you multiply this by 10 years you don't even get a change of frequency of 1/1000 of a second and in the graph it...
  5. victorhugo

    I Why don't general relativity and quantum physics agree?

    I always hear that the two 'don't match' and disagree, but never in what... Someone mind explaining?
  6. Barnak

    A Color of Deep Space: Distribution of Light Wavelengths

    I'm looking for the distribution of all wavelengths (or frequencies) of light that a stationary observer would receive at his location (at ##r = 0## and time ##t_0##), from all light sources emitting a single wavelength ##\lambda_{\text{e}}## (or angular frequency ##\omega_{\text{e}}##). The...
  7. Devin

    I Stress Energy Tensor for Oscillator: Setup for Electron in E-Field

    How would one go about setting up the stress energy tensor for a particle, say an electron subjected to electric an electric field that makes the particle oscillate with frequency \omega?
  8. D

    Four-Velocity and Schwartzchild Metric

    Homework Statement What is the Schwartzchild metric. Calculus the 4-velocity of a stationary observer in this spacetime (u). Show that u2 = c2. Homework Equations Schwartzchild Metric d{s^2} = {c^2}\left( {1 - \frac{{2\mu }}{r}} \right)d{t^2} - {\left( {1 - \frac{{2\mu }}{r}} \right)^{ -...
  9. F

    I Formation of Bound Systems, Stars & Galaxies in General Relativity

    In particular how does matter "clump" together to form stars and planets, and how do Galaxy/star systems form? For the latter question is the answer simply that near massive enough bodies, the spacetime curvature is significant enough that the geodesics within its vicinity are closed curves...
  10. K

    Acceleration in a new Coordinate System - General Relativity

    Homework Statement Below: Jac = Jacobian matrix; ξ = d/dφ for some continuous parameter φ which labels different points on the worldline. (I'm sorry for my poor English.) Consider a new coordinate system xµ' which differs from the original Cartesian coordinate system xµ; the Cartesian...
  11. P

    A Did Einstein Disbelieve in General Relativity Geometry?

    I have read this paper http://www.sciencedirect.com/science/article/pii/S1355219813000695 that the author try to said that einstein not believe that gravity is not cause the space time curvature. I want to know that this is true or not. Because when I have read about general relativity I always...
  12. haushofer

    Insights General Relativity as a Gauge Theory - Comments

    haushofer submitted a new PF Insights post General Relativity as a Gauge Theory Continue reading the Original PF Insights Post.
  13. L

    A Ricci Form Notation: Need Help Understanding

    The material I am studying express the Ricci form as ##R = i{R_{\mu \bar \nu }}d{z^\mu } \wedge d{{\bar z}^\nu } = i\partial \partial \log G## where ##G## is the determinant of metric tensor, but I am not sure what does ##\log G## here, can anybody help?
  14. Y

    A Capture by Gravitational Radiation in 2-Body System?

    Is it possible for enough energy to be dissipated in the form of gravitational radiation in a two-body system to allow for capture? From what I remember, you would need extremely massive bodies passing extremely close to each other: I'd like to know how massive and how close. It has been a few...
  15. felici95

    I Dimensionless Time: Rindler & Minkowski Spacetime

    What does the dimensionless time in Rindler spacetime signifies? And how something dimensionless can be regarded as time and coupled up with proper distance in Minkowski spacetime? (Page 7: https://www.perimeterinstitute.ca/images/files/black_holes_and_holography_course_notes.pdf )
  16. Indiana

    A Where does statistical physics/mechanics fit in with QFT,GR?

    We have two theories namely,Quantum Field Theory which works very well at sub-atomic scales, and the General Relativity which works very well at very large scales.So, my question is where does statistical physics/mechanics fit in? What role statistical physics/mechanics play in today's modern...
  17. T

    I How does parallel transportation relates to Rieman Manifold?

    Source: Basically the video talk about how moving from A to A'(which is basically A) in an anticlockwise manner will give a vector that is different from when the vector is originally in A in curved space. $$[(v_C-v_D)-(v_B-v_A)]$$ will equal zero in flat space...
  18. C

    I Ivanenko, Logunov and even Zelmanov

    What do you think about the work done by these Russians to give alternative formulations to General Relativity?
  19. N

    I How Is Proper Acceleration Expressed in General Relativity?

    I know that in Special Relativity, proper acceleration is understood as: a*ga^3, where ga is the lorentz term and 'a' is coordinate acceleration. Is there a corresponding expression for proper acceleration within the various geodesics that result from solutions to Einstein's Field Equations? If...
  20. A

    I Spin Foam models in Loop Quantum Gravity

    Hi all, I fairly basic question about spin foam models in loop quantum gravity. I just want to verify that spin foams represent effectively represent all of spacetime (in a quantum form), and that the idea is that general relativity can be obtained in the classical limit? Not sure if that's...
  21. P

    I Detecting Earth in an Elevator: Thought Experiment

    I have in mind thought experiment where physicist is in elevator falling towards the Earth. Question would be if he is not allowed to look outside, how would he detect the presence of the planet? Let's not take in consideration tidal forces and assume he is taking local measurements during small...
  22. K

    Relativity A First Course in General Relativity

    For those who have read Schutz' book A First Course in General Relativity. Can this book be considered as a deep approach on the subject? Edit --- Do you think I will become a "expert" in general relativity just by reading books like this one I mentioned above? What time it take for learning...
  23. D

    I Energy-momentum tensor and Friedmann Equations

    Hi everyone, I want to derive the Friedmann equations from Einstein Field Equations. However, I have a problem that stems from the energy-momentum tensor. I am also trying to keep track of ## c^2 ## terms. FRW Metric: $$ ds^2= -c^2dt^2 + a^2(t) \left( {\frac{dr^2}{1-kr^2} + r^2 d\theta^2 + r^2...
  24. V

    I Measuring Coordinates in Strong Gravity: Schwarzschild Metric

    We know that Schwarzschild metric describes an asymptotically flat spacetime. This means that far away from the event horizon we can safely interpret the ##r## coordinate as distance from the center. But when close enough to the event horizon the curvature becomes significant and our common...
  25. E

    I Vacuum solutions in general relativity

    If we look Einstein equation ##G_{\mu\nu}=0##, which nontrivial aspects it can gives? One phenomenon is gravitational wave. I suppose that we are also free at initial conditions for this equation, thus we can begin with curved space time? What else?
  26. V

    A Time dilation for the clock in the orbit

    Suppose that we want to compute the total time dilation for a clock located in an orbiting satellite relative to the clock in our cell phone on the ground. Consider two different approaches below. 1. Use special relativity and compute time contraction due to velocity. Use approximation of...
  27. V

    A Geometry and integral laws of physics

    Reading the English translation of Einstein's seminal paper on GR. http://einsteinpapers.press.princeton.edu/vol6-trans/90?ajax This paragraph below on p78 doesn't make much sense to me. Could you provide a second English translation or even adding math notation. "Before Maxwell, the laws...
  28. V

    A Geodesic defined for a non affine parameter

    The geodesic general condition, i.e. for a non affine parameter, is that the directional covariant derivative is an operator which scales the tangent vector: $$\zeta^{\mu}\nabla_{\mu}\zeta_{\nu}=\eta(\alpha)\zeta_{\nu}$$ I have three related questions. When $$\alpha$$ is an affine parameter...
  29. A

    B General Relativity and Newtonian Mechanics

    Hello, I wanted to know how Einstein's General Relativity and its equations simplify to Newton's Universal Law. Einstein's equation is obviously a much more generalized version of Newton's law and gives much more accurate predictions that Newton's laws even if we don't think of Newton's gravity...
  30. tomdodd4598

    I Special Relativity Approximation of Gravitation

    Hey there, I have two questions - the first is about an approximation of a central gravitational force on a particle (of small mass) based on special relativity, and the second is about the legitimacy of a Lagrangian I'm using to calculate the motion of a particle in the Schwarzschild metric...
  31. RJLiberator

    General Relativity Problem (frames of reference)

    Homework Statement A clock moving at v = (3/5)c reads 12:00 as it passes us in our frame of reference, how far away will it be (in light hours) when it reads 1:00. Homework Equations I denote a prime to mean the reference frame of the clock at rest. I use regular lettering to denote 'our'...
  32. S

    A Solve Gravitational Interferometer & Geodesics

    I was trying to solve this excercise: Now I was able to find the eq. of geodetics (or directly by Christoffel formulas calculation or by the Lagrangian for a point particle). And I verified that such space constant coordinate point is a geodetic. Now, for the second point I...
  33. F

    A Numerical integration of motion

    Hi,I'd like to build a simulation (realtime) of space ships near a black hole (neutral, still or rotating possibly). Key features would be: 1) the ships are test particles that do not affect the metric a) possibly test rigid-bodies with GR consistent rotational DOF. 2) the ships can fire...
  34. e2m2a

    I General Relativity vs Newtonian Weak Field: G Force?

    When does GR apply in gravitational fields as opposed to Newtonian gravitation? Another words, what would be the strength of the graviatational field before we abandon Newtonian gravity and start implementing GR? 10 g's, 20 g's?
  35. Jackie CH Liu

    A A Quantum Theory of Spacetime, the Physical Reality of Cross

    I just want to share my paper I recently wrote. I am trying to submit for publication: [Reference to unpublished paper deleted]
  36. Domenico94

    A Gravitational law of induction

    By reading on the internet I ve found various websites talking about the relation between gravitation and electromagnetism, and in particular, under: - "Small" Gravitational fields -"small" changes in energy with respect to time, The linearized enstein' s field equation becomes pretty much...
  37. almarpa

    Relativity Introduction to GR. ¿Gron or Collier?

    Hello all. I am self teaching physics, and after completing Classical Mechanics (Special Relativity included), Classical EM and an introductory course to QM, I would like to take a very introductory look to General Relativity. With this purpose in mind, I have chosen 2 books, and I would like...
  38. A

    B Euler-Lagrange equation for calculating geodesics

    Hello I am little bit confused about lagrange approximation to geodesic equation: So we have lagrange equal to L=gμνd/dxμd/dxν And we have Euler-Lagrange equation:∂L/∂xμ-d/dt ∂/∂x(dot)μ=0 And x(dot)μ=dxμ/dτ. How do I find the value of x(dot)μ?
  39. J

    Courses Prerequisite to General Relativity/Cosmology Undergad course

    Hello, If anyone could help me with the prerequitisetes for an undergraduate General Relativity and Cosmology course I will enroll into, It will be much appreciated. The syllabus is the following(sorry for the rough translation): -Review of Special Relativity -Spacetime in GR -Geodesics...
  40. Diego Berdeja

    I Lorentz Transformations in the context of tensor analysis

    Hello everyone, There is something that has been bugging me for a long time about the meaning of Lorentz Transformations when looked at in the context of tensor analysis. I will try to be as clear as possible while at the same time remaining faithful to the train of thought that brought me...
  41. mgkii

    I Two black holes colliding - visual

    There's lots of other questions on the forum about 2 black holes, but I think this is different - and I can't get my head around which outcome is consistent with GR. Black holes here are simplistic - non-rotating and let's assume with a tiny accretion disk; just enough grains of matter to allow...
  42. B

    Insights Precession in Special and General Relativity - Comments

    Bill_K submitted a new PF Insights post https://www.physicsforums.com/insights/precession-special-general-relativity/ https://www.physicsforums.com/insights/precession-special-general-relativity/
  43. K

    A CPT symmetry and antimatter gravity in general relativity

    CPT symmetry and antimatter gravity in general relativity M. Villata Published 28 March 2011 • Europhysics Letters Association EPL (Europhysics Letters), Volume 94, Number 2 Abstract The gravitational behavior of antimatter is still unknown. While we may be confident that antimatter is...
  44. directbydirecct

    A Deriving Amplification of Images in Schwartzschild Metric

    In the paper Strong field limit of black hole gravitational lensing, the amplification of images in the Schwartzschild metric was given by $$ \frac{1}{\beta}\sqrt{\frac{2\,D_{LS}}{D_{OL}D_{OS}}} $$However the authors did not derive this expression or explain its origin. Does anyone know how to...
  45. P

    I Can one determine the velocity of a photon in the fourth dimension using limits?

    Can one shed light on the velocity of the photon through the fourth dimension x4 using limits? To begin with, please study the mathematics from Brian Greene’s book An Elegant Universe. The upshot is that the faster an object moves through space, the slower it moves through the fourth...
  46. J

    Relativity General Relativity by Hobson, Lasenby and Efstathiou

    Hello, Is the book General Relativity by Hobson, Lasenby and Efstathiou good in the sense that is intuitive on the mathematics AND physics that it presents? Please vote and if you could also comment your opinion it would be much appreciated. Thanks!
  47. Cosmology2015

    I How to measure time in the early universe?

    I would like to study more about the notion of time in modern physics. In particular, I would like to understand better the following question: how does one measure the time in the early universe? To measure time one needs to have clocks. A natural choice to be used as clocks would be particles...
  48. A

    A Prep for Hawking/Ellis: Point Set Topology Needed

    I'm trying to prepare to read The Large Scale Structure Of Space-time by Hawking and Ellis. I've been reading a General Topology textbook since the authors say "While we expect that most of our readers will have some acquaintance with General Relativity, we have endeavored to write this book so...
  49. A

    I What is the Concept of Velocity and Acceleration in General Relativity?

    I am hoping someone can clarify some confusion I have. It is my understanding that there is no such thing as absolute velocity or acceleration in GR. If one observer is moving near the speed of light and the other is stationary each observer will see the other as in motion. But if they each...
  50. A

    I What are the independent components of the Riemann tensor

    What 20 index combinations yield Riemann tensor components (that are not identically zero) from which the rest of the tensor components can be determined?
Back
Top