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. L

    Differentiating with coordinate transformations

    T = (x+\frac{1}{\alpha}) sinh(\alpha t) X = (x+\frac{1}{\alpha}) cosh(\alpha t) - \frac{1}{\alpha} Objective is to show that ds^2 = -(1 +\alpha x)^2 dt^2 + dx^2 via finding dT and dX and inserting them into ds^2 = -dT^2 + dX^2 Incorrect attempt #1: dT= (dx+\frac{1}{\alpha})...
  2. N

    Prerequisites for General Relativity (Advice needed)

    Summary: At this point, I am thorough with single variable, multivariable calculus, differential equations, linear algebra and basic concepts of point-set topology and tensor analysis. To learn General Relativity along-with its mathematical rigor, what are the topics I should first be thorough...
  3. abby11

    A Derive Radial Momentum Eq. in Kerr Geometry

    I am trying to derive the radial momentum equation in the equatorial Kerr geometry obtained from the equation $$ (P+\rho)u^\nu u^r_{;\nu}+(g^{r\nu}+u^ru^\nu)P_{,r}=0 \qquad $$. Expressing the first term in the equation as $$ (P+\rho)u^\nu u^r_{;\nu}=(P+\rho)u^r u^r_{;r} $$ I obtained the...
  4. Vick

    A Anisotropic Universe and Friedmann Equations

    The Friedman Equations is based on the cosmological principle, which states that the universe at sufficiently large scale is homogeneous and isotropic. But what if, as an hypothesis, the universe was anisotropic and the clustering of masses are aligned to an arbitrary axis (axial pole), how...
  5. M

    I Why does quantum mechanics believe that gravity is a field?

    According to general relativity, gravity is simply the side-effect of bending the geometry of space-time. As a thought experiment imagine a 3D image being projected from a 2D hologram - the distance between the actual 2D pixels in the 2D plane always remains constant, yet depending on the shape...
  6. cordless03

    B Finding Flaws in General Relativity: A Question of Knowledge

    This thread is supposed to be about finding flaws in General Relativity, but the way these people talk they sound like they have no real knowledge of GR. I was just curious if any of you guys could explain further.
  7. Martin Scholtz

    What Research Does Martin Scholtz Conduct in Gravitational Physics?

    My name is Martin Scholtz and I am a postdoc researcher at the Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic. I'm working mainly in the area of gravitational physics, but I am interested in different topics as well, see tags...
  8. D

    I Deriving tensor transformation laws

    Hi, I'm worried I've got a grave misunderstanding. Also, throughout this post, a prime mark (') will indicate the transformed versions of my tensor, coordinates, etc. I'm going to define a tensor. $$T^\mu_\nu \partial_\mu \otimes dx^\nu$$ Now I'd like to investigate how the tensor transforms...
  9. M

    A Developments to unify quantum theory with General Relativity?

    Have there been any recent developments in the attempt to unify the standard model of quantum theory with General Relativity? It appears the no progress has been made recently in string theory or loop quantum gravity.
  10. Bob R

    B Confirm General Relativity: Eddington's Starlight Experiment

    If Earth's motion about the sun is described by General Relativity why was Eddington's experiment with the bending of starlight needed to confirm the theory? In other words, don't we see enough common phenomena in our every day experiences to confirm GR without verifying subtle phenomena such as...
  11. SJay16

    B How well should Astronomers know General Relativity?

    I know that it would vary depending on the type of research a specific astronomer would be doing ( Astrophysics/Cosmology research versus an Astronomer researching exoplanets ) ; but in your opinion, “how much” or “how well” should an Astronomer with a graduate degree in Astronomy know General...
  12. Jason Bennett

    I Alternative form of geodesic equation for calculating Christoffels

    From Thomas Moore A General Relativity Workbook I have the geodesic equation as, $$ 0=\frac{d}{d \tau} (g_{\alpha \beta} \frac{dx^\beta}{d \tau}) - \frac{1}{2} \partial_\alpha g_{\mu\nu} \frac{dx^\mu}{d \tau} \frac{dx^\nu}{d \tau} $$ as well as $$ 0= \frac{d^2x^\gamma}{d \tau^2} +...
  13. JD_PM

    A Understanding gravitational waves (GR)

    I am reading the following paper on the basic physics of a binary black hole merger: https://arxiv.org/ftp/arxiv/papers/1608/1608.01940.pdf Imagine two black holes orbiting each other until a point they merge. As you can see in Figure 1, the wave period is decreasing and thus the frequency...
  14. nearc

    B Prereqs for Posting in Special & General Relativity

    i am far from an expert in Special and General Relativity, however, my attempts to learn from this forum are hampered by the large volume of posts involving common misconceptions and lack of understanding of the material. while the members of the forums patiently [usually] help our novice and...
  15. SJay16

    Courses How difficult is an undergraduate course in GR?

    Just wondering if I'm going to be in over my head here, as I'm not sure what to expect. A notoriously "difficult" professor as my school is teaching a senior level undergraduate course "Introduction to General Relativity Physical consequences of Einstein's equations, including the principle of...
  16. The black vegetable

    I Orthonormal Basis - Definition & Examples

    Is this correct? If not any hints on how to find Many thanks
  17. L

    How to pick a concrete PhD objective in this QFT/Gravity formalism?

    I have a major in Mathematics and Mathematical Physics and I'm finishing a masters in Physics (just finishing to write down the dissertation really). I have also already enrolled the PhD course so that I need now to pick an advisor and a theme before june. My main interest since the early days...
  18. B

    I Issue With Derivation of Gravitational Time Dilation

    Why do we use the equation ##\frac {1}{2}mv^2 = \frac {GmM}{r}## to derive potential velocity, and then put that in the Lorentz factor in order to derive gravitational time dilation? Shouldn't we be using the relativistic definition of kinetic energy -> ##mc^2(\gamma - 1)## to derive the...
  19. haael

    A What does the image of the black hole say about general relativity?

    We all heard about the "photo of black hole". My question is: did this image show any hints of physics beyond general relativity? I read once (not sure where) that the apparent size of black hole shadow is very sensitive to corrections to general relativity. Add some minor correction and the...
  20. J

    I Does the Friedmann vacuum equation have a linear solution?

    Does the Friedmann vacuum equation have a linear solution rather than an exponential one? Using natural units one can write Friedmann's equation for the vacuum as $$ \begin{eqnarray*} \left(\frac{\dot a}{a}\right)^2 &=& \frac{8\pi G}{3}\rho_{vac}\\\tag{1} &=& L^2 \left(\frac{\rho_0}{L^4}\right)...
  21. P

    I Confusion about index notation and operations of GR

    Hello, I am an undergrad currently trying to understand General Relativity. I am reading Sean Carroll's Spacetime and Geometry and I understand the physics (to a certain degree) but I am having trouble understanding the notation used as well as the ideas for tensors, dual vectors and the...
  22. S

    A Penrose diagram of black hole with a changing event horizon

    Dear all, I have a question on Penrose diagrams. Consider a collapsing star that forms a black hole with a Schwarzschild radius normalized to 1. What happens in the Penrose diagram when additional matter falls in? I suspect the diagram then has to look like this : When the outer shell (second...
  23. PeterDonis

    Insights Fermi-Walker Transport in Kerr Spacetime - Comments

    Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Kerr Spacetime Continue reading the Original Blog Post.
  24. T

    I Why do particles around us have finite momenta?

    Since there is no privileged inertial frame, I would have expected the first particles in the universe to have no particular bias in their momenta. Relative to an observer I would expect the distribution to be uniform and unbounded. The mean momentum of the initial particles relative to an...
  25. M

    I General Relativity and light deflection

    I am a student of physics at a local Junior College in Mendham NJ and am planning on transferring to a 4 year program at the University of Alabama in a year. Iam having a bit of a difficult time understanding general relativity. Why does a photon bend twice as much under a gravitational field...
  26. PeterDonis

    Insights Fermi-Walker Transport in Schwarzschild Spacetime - Comments

    Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Schwarzschild Spacetime Continue reading the Original Blog Post.
  27. PeterDonis

    Insights How to Study Fermi-Walker Transport in Minkowski Spacetime

    Greg Bernhardt submitted a new blog post How to Study Fermi-Walker Transport in Minkowski Spacetime Continue reading the Original Blog Post.
  28. Cerenkov

    B General Relativity: Finding Info on Interpretation

    Hello. I have some questions about general relativity that (I hope) will be permitted in this forum. Not long ago I discovered that there is more than one interpretation of GR. Now, I believe that the issue of interpretation is considered to be philosophy and therefore off topic. If that's...
  29. J

    I Feynman-Heaviside formula and Mach's principle

    I was wondering if the [Feynman-Heaviside formula](http://www.feynmanlectures.caltech.edu/II_21.html) for the electric field of a moving charge could be used to write down the force/reaction force between charges ##q_1## and ##q_2## in a Machian purely relational way. The retarded electric...
  30. S

    B Big Rip Theory & Black Holes: Relativity Explained

    According to the Big rip theory if Black holes tear apart after a very long time, then according to the theory of relativity an object that reaches the event horizon should see time passing infinitelty and by the time the object was swallowed wouldn't the black hole not exist anymore because of...
  31. F

    I Is there a zero-mass, vacuum Schwarzschild GR solution?

    The Schwarzschild solution of the Einstein Equation of GR is said to be the only time-independent matter-free solution of that equation. In this usage, does “matter-free solution” mean without matter everywhere except at the singularity of the solution? I thought that the only solutions of the...
  32. MatthewNITX

    Relativity Suggestions for a Physics Textbook on Special & General Relativity

    Hey my fellow physics-students/physicists. I'd like to ask if you guys could suggest me a textbook/s that sufficient for integrated course of "special" and "general relativity". More precisely, That contain about: Introduction about the birth of relativity and principle, and the transformation...
  33. robphy

    B General Relativity as a Challenge for Physics Education

    This week I am at "General Relativity as a Challenge for Physics Education" 690. WE-Heraeus-Seminar https://www.we-heraeus-stiftung.de/veranstaltungen/seminare/2019/general-relativity-as-a-challenge-for-physics-education/ (...
  34. K

    I Allowed fields in General Relativity

    How do you know what fields can be coupled with the gravitational field? Is there a general procedure for knowing it or we have to try out and see whether it makes sense or not?
  35. PeterDonis

    I General Relativity rocket puzzle

    A while back I posted a black hole horizon puzzle. This is another puzzle in the same general spirit. It is based on the scenario described in this old PF thread: https://www.physicsforums.com/threads/a-flaw-of-general-relativity.115418/ Needless to say, as was the case with my previous...
  36. L

    I Massive Particles in Sonic & Slow Light Black Holes

    I am working on a research project where I intend to describe what the Penrose process would like in a sonic black hole. I have found what a rotating (Kerr) black hole looks like in the sonic analog: https://arxiv.org/pdf/1802.08306.pdf I have also found that the analog of massless particles...
  37. K

    I Allowed transformations in General Relativity

    Does General Relativity allow for transformations which are not isometries of the metric?
  38. L

    I What does coupling mean in physics?

    I am reading Carroll’s Spacetime and Geometry, and I have seen the word “coupled” used multiple times in seemingly different ways. I have gotten the sense that it means some sort of interaction between particles, but Carroll refers to coupling between matter fields and the curvature of...
  39. cianfa72

    I About spacetime coordinate systems

    Hi, There is a point that, in my opinion, is not quite emphasized in the context of general relativity. It is the notion of spacetime coordinate systems that from the very foundation of general relativity are assumed to be all on the same footing. Nevertheless I believe each of them has to be...
  40. M

    A Orbit velocity in Schwarzschild metric?

    Hi, I'm trying to deduce orbit velocity of a particle with mass from Schwarzschild metric. I know for Newtonian gravity it is: $$v^2=GM\left(\frac{2}{r}-\frac{1}{a}\right)$$ The so called vis-viva equation. Where ##a## is the length of the semi-major axis of the orbit. For Schwarzschild metric...
  41. FourEyedRaven

    Relativity Raychaudhuri - General Relativity, Astrophysics, & Cosmology

    Hello. The book "General Relativity, Astrophysics, and Cosmology", by Raychaudhuri, et al., looks like a good compact exposition of GR, astrophysics and cosmology, which is exactly the kind of book I'm looking for. What do you think of this book? Thank you in advance.
  42. N

    I Gravity in General Relativity: Explaining Acceleration

    Greetings: I can understand that an object's trajectory curves about a greater mass (e. g., satellite in Earth's orbit). The spacetime is curved via the great mass and the moving object simply follows the curvature. My problem is this: Why does a stationary object at a short distance from...
  43. D

    I Orbital Simulator with general relativity

    Is it possible to calculate with precision the orbits of the Earth, Moon and Sun with general relativity instead of Newtonian Physics? How would this work? Would the software have to record past positions of each body and have the Earth be attracted to the old sun's position 8 minutes ago...
  44. m4r35n357

    I Solve General Relativity "Paradox" w/ Automatic Diff. ODE Solver

    After making a couple of comments on this StackExchange question, and pointing yet again to this article, a thought occurred to me. I have been working on an Automatic Differentiation based ODE solver and equation analyzer, mentioned in this thread. Why not use it to solve equation (7) in the...
  45. F

    I Computer Performance Evaluation (CPE)

    I would like to know if there are any Physics Instructors or Professors who may believe that Queuing Theory as well as Relativity Theory may be relevant to CPE where communications platforms are moving at relativistic velocities with respect to (wrt) each other?
  46. L

    I Do we have to accept the physical existence of time?

    So, I am confused about the following.I learned in high school and in my first year of university that there is something called time dilation that observers observe that time is slower for objects that are moving faster. As in if there were two initially synchronized clocks that you could...
  47. T

    Are there job opportunities in general relativity for theoretical researchers?

    Are there a lot of theoretical research jobs in general relativity or would that be too hard to find?
  48. The black vegetable

    I Solve General Relativity Equation: Steps & Tips

    Maybe I'm just being stupid, missing something simple ? How do you get from the top two equations to the second equation? Many thanks
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