General relativity Definition and 999 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. Onyx

    A What kind of topology change does this Lorentzian metric describe?

    Looking at this paper, what sort of spatial topology change does the lorentzian metric (the first one presented) describe? Does it describe the transition from spatial connectedness to disconnectedness with time? All I know is that there is some topology change involved, but I don’t see the...
  2. S

    Is the Lie derivative a tensor itself?

    Hi everyone! A few days ago in General Relativity class, the professor introduced the concept of Lie derivative and at the end he mentioned that the Lie derivative was a tensor itself. I've been looking everywhere, but I only find how it acts on vectors, tensors, etc. Does anyone know of any...
  3. Tribal Blue

    Exploring the Mystical World of Science Brings New Inspiration

    Hello! I am a creator who loves the fascinating world of science. I enjoy exploring science from a unique angle, which often leads to new and creative ideas. While some of these ideas can be speculative and challenging to prove, I make sure they align with scientific principles and logical...
  4. S

    B Would an object in orbit change facing or orientation?

    Assume a 2D XY grid, and we'll label the obvious directions N, S, E, and W. Assume an object is just going along a straight line from S to N in flat space with no forces acting on it or imparted to it, including rotational. Let's assume some kind of mark on it so we can keep track of...
  5. Clvrhammer

    I Definition of time-independent scalar field in GR

    I was wondering how the notion of a time-independent field translates into the context of General Relativity. In order to specify my confusion, consider a scalar field ##\phi## in Schwarzschild spacetime with usual coordinates ##(t,r,\theta,\phi)##. Its metric is $$g = - f(r) \, dt^2 + f(r)^{-1}...
  6. Kostik

    A How to show spin ##= \pm 2/\omega## for a circ-polarized gravity wave

    It is well understood that an infinite monochromatic, circularly-polarized electromagnetic plane wave has no angular momentum density. However, a finite monochromatic, circularly-polarized electromagnetic plane wave packet does have an angular momentum density, arising from effects at the border...
  7. Clvrhammer

    A Stationary solutions to Klein Gordon equation in spherical symmetry

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  8. LazyPhysicist1

    I Solution To Photon Trajectory Equation

    Using the null geodesic and the Schwarzschild metric, this differential equation for photon trajectory near a mass can be derived, where u is r_s /2r: Though this nonlinear ode is fairly easy to approximate (which I already have), I'm looking for an analytic solution or an approximate...
  9. S

    I Question on halos of matter made from massive and stable particles?

    Consider a halo made up from massive and stable particles like neutrinos* (let's not consider protons which, although we don't have any experimental evidence showing that they are unstable and decaying, there are some GUTs proposing theoretical mechanisms where they could decay over extremely...
  10. P

    A New Adler book on GR: Why do these coefficients go to zero?

    This is page 73 of the book. As you can see, the mixed derivatives with the affine connections vanish in the second term. Why does that happen? This is used to prove that the connections are not a tensor, and i figured you could also reason it out even without making those terms vanish. OBS...
  11. ohwilleke

    B Why do people care about vacuum solutions in GR?

    I understand that there are vacuum solutions of the equations of general relativity (GR) (i.e. equations with no mass-energy content contributing to the stress-energy tensor), that are studied by physicists interested in GR. I don't understand why these are studied or what purpose they serve...
  12. F

    A Horndeski: denominator null implies an infinite quantity

    Core Equation:I am examining the following equation: ## \frac{\partial \mathcal{A}_{\mu \nu}}{\partial g_{\rho \sigma, \tau \pi \lambda}} \frac{\partial g_{\rho \sigma, \tau \pi \lambda}}{\partial g_{\rho^{\prime} \sigma^{\prime}, \tau^{\prime} \pi^{\prime} \lambda^{\prime}}} = \frac{\partial...
  13. Kostik

    A Dirac "GTR" Eq. 27.11 -- how to show that a boundary term vanishes?

    In Dirac's "General Theory of Relativity", p. 53, eq. (27.11), Dirac is deriving Einstein's field equations and the geodesic equation from the variation ##\delta(I_g+I_m)=0## of the actions for gravity and matter. Here ##p^\mu=\rho v^\mu \sqrt{-g}## is the momentum of an element of matter. He...
  14. cianfa72

    I Gravitational wave propagation in GR

    Hi, I'd like to discuss in this thread the propagation of Gravitational Waves (GW) in the context of GR. Just to fix ideas, let's consider a FW spacetime. It is not stationary (even less static), however the timelike congruence of "comoving observers" is hypersurface orthogonal. Suppose at a...
  15. J

    A body at rest in Doran and Boyer-Lindquist coordinates

    I read this question in the second edition of "Exploring Black Holes" by Wheeler, Taylor & Bertschinger. The book can be freely accessed and downloaded from the author's website. Chapter 17 deals with Kerr's solution on the equatorial slice ## \theta = 0 ##. In Doran coordinates, the 2+1 metric...
  16. PhysicsEnjoyer31415

    I Einstein field equations

  17. S

    I Can there be structures made from neutrinos with angular momentum?

    Would it be possible to eventually have structures made from neutrinos somewhere in the universe, as it is indicated in this question (https://physics.stackexchange.com/questions/80390/are-neutrino-stars-theoretically-possible), like halos of neutrino gas surrounding the center of galaxies...
  18. jack action

    Intro Physics Physics for babies

    Would you buy these books?
  19. P

    Programs Should I do a math or an astronomy double major for general relativity?

    Hi! I'm going into college during the fall, (Stony Brook University in the US) and I want to research general relativity in the future. I can choose to do an astronomy or math double major alongside my physics degree, and I want to know which degree will best prepare me for a graduate program in GR
  20. I

    I Handshake paradox involving the Starship Enterprise

    suppose the enterprise departs from planet earth on a mission the the other side of the milky way at 90% of the speed of light; since time is dilated while cpt Kirk drinks coffe on planet earth some time passes (let's say 1h). Approaching mars captain Kirk orders dt. Spock to land on Mars with...
  21. cianfa72

    I Meaning of the distance between galactic objects in GR

    Hi, I was thinking about the claim that for instance Sagittarius A* (Sgr A*) black hole is a at 26996±29 light years from the Earth from a GR point of view. Assuming a FLRW model for the Universe, maybe the above meaning is that at a given cosmological time ##t## (the "present" time) the proper...
  22. S

    I Can there be slowly-falling accretion disks in black holes?

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  23. Onyx

    I Israel Junction Conditions: Finding Continuous Metric Across Shell

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  24. S

    I Does Kerr's argument against singularities apply to all black holes?

    Roy Kerr has recently written a preprint (https://arxiv.org/abs/2312.00841) in which he strongly argues against the possible existence of singularities inside Black Holes. I've read that his arguments are really powerful and that he is most likely right. But, does it mean that Kerr has...
  25. N

    A Coupling torsion to electromagnetism and torsion tensor decomposition

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  26. cianfa72

    I Galaxy recession and Universe expansion

    Hi, I'm aware of the measured recession of the galaxies in our universe and the universe expansion itself cannot be understood as an "ordinary" velocity/speed (for instance in the FRW solutions of Einstein's equations). Can you kindly help me clarify this topic ? Thank you.
  27. S

    I The Evolution of Galactic Scale Cosmic Voids

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  28. S

    I Do the Sachs-Wolfe and Rees-Sciama Effects Influence Matter?

    CMB photons can be affected by the expansion of the universe through the linear integrated Sachs-Wolfe effect (ISW) [1] and the non-linear ISW effect or also called Rees-Sciama effect [1]. In particular, according to the ISW effect, the photons crossing superclusters would leave them having a...
  29. m082844

    I Why doesn't relativity of simultaneity lead to a contradiction?

    I cannot get the following out of my head. Suppose this situation. Three frames, with varying velocities, simultaneously intersect their origins at the same time and place, making this point and time x0=0 and t0=0. These frames... let's call them observers. These observers have an agreed upon...
  30. I

    Problems with the Riemann tensor in general relativity

    After Taylor expansion and using equations (2), I have no problem getting to equation (1). Now obviously I have to somehow use (3.71) ,which I do know how, to derive to express the second order derivative. On the internet I found equation (3), and I have tried to understand where this comes from...
  31. K

    I Question about Einstein's famous elevator experiment

    Hi, In Einstein's famous elevator experiment, someone in the elevator cannot tell if the acceleration they experience is from the gravity of a nearby large mass, or from their own change of velocity under the influence of some external force. But if there is an external force accelerating...
  32. zinn

    I Separation angle between pulsars detecting Gravitational Waves

    I’m trying to understand the Hellings and Downs curve that is being used to argue for the existence of a gravitational wave background ([NANOGrav article][1]). How can it be that the angle between two pulsars is the only variable that determines if the gravitational waves will interfere...
  33. K

    I Energy conservation in general relativity

    Is energy conserved in general relativity? I have read most of the posts here that address this. But it isn't clear to me, what most people say is that energy is conserved locally but it can't be defined globally, some people say this means that energy is not conserved in GE while others argue...
  34. P

    A Correspondence between areal radius differences and proper distances

    Other ways of wording this finding about the extended SC (Schwarzschild) spacetime: - in the local frame of a free faller, radial distance is given r coordinate difference - in either Fermi-normal coordinates, or Riemann-Normal coordinates built from a free faller at an event, coordinate...
  35. F

    I Variation of the lightning train thought experiment

    Hi all, I've been going over some special relativity as it's a topic I never really studied during my younger years and wanted to get to grips with it, especially since it's such a fundamental part of our understanding of the cosmos. I was reading about Einsteins train lightning thought...
  36. cianfa72

    I Invariant definition of acceleration in Newtonian physics vs proper acceleration in GR

    Does it exist an invariant way to define acceleration in Newton physics like the proper acceleration in GR ? In Newton physics if an accelerometer attached to an object reads 0 it does not mean it is actually not accelerating (since gravity is a force). To define inertial motion the concept of...
  37. H

    I Does dark-energy require a source of energy?

    In the Lamda-CDM model of cosmology, dark-energy is explained by a Lamda like curvature of space-time. In this description, space-time is curved in such a way as to cause a gentle outward repulsive force on the large scale, expanding all of the universe over time. This is one cause of the...
  38. Bosko

    I A mirror behind the event horizon

    Thought experiment: What will happen if you place a mirror behind the event horizon and turn on the light in its direction?
  39. Tommolo

    A A question about tensor calculus in Von Neumann algebra (W*)

    Hi there, have a wonderful next year! I'm here because I have a doubt. I was trying to generalize the Einstein Field Equation for Von Neumann W* Algebra, which is related with non-integer, non always positive degrees of freedom. In particular, with the sum of positive and negative fractal...
  40. bhobba

    A The Emergence of Space-time in String Theory

    A few yesrs ago now I read a First Course in String Theory. In that book strings were part of normal space-time plus for consitency some extra dimensions. Spin 2 partices natually emerged and so did GR. I didnt think anything of it at the time (pun intended), but I recently saw a...
  41. G

    Why Are My Geodesic Calculations Dependent on an Unknown Function?

    For (a) and (b), since the geodesic is not affinely parametrised, we have that ##t^a\nabla_a t^b = f(\lambda) t^b##, for some function f. As a results, for (a) I get that ##t^a \nabla_a \epsilon = 2 f(\lambda) \epsilon##. And for (b) I get that ##t^a \nabla_a p = f(\lambda) p##. (I can write...
  42. A

    Physics Mediocre, But Passionate Physics Student--Jobs in General Relativity?

    I'm a mediocre physics student (at best) at an Ivy League institution, and I'm passionate about general relativity. My dream is simply to do research in the field, even though I will never be a superstar or pioneer. Finally, I'm planning to complete a Master's in astrophysics or physics...
  43. cianfa72

    I General Relativity and the precession of the perihelion of Mercury

    Hi, as test of GR I'm aware of there is the "anomalous" precession of the perihelion of Mercury. My question is: in which coordinate system are the previsions of GR verified concerning the above ? Thanks.
  44. cianfa72

    I Wald synchronous reference frame proof

    Hi, on Wald's book on GR there is a claim at pag. 43 about the construction of synchronous reference frame (i.e. Gaussian coordinate chart) in a finite region of any spacetime. In particular he says: $$n^b\nabla_b (n_aX^a)=n_aX^b\nabla_b \, n^a$$Then he claims from Leibnitz rule the above equals...
  45. Hak

    I Special Relativity: an ideal experiment

    Let me preface this by saying that I do not claim to dismantle relativity. That said, in reading the Feynman I came across an ideal experiment that is not entirely clear to me. The context is the usual two spacecraft moving at relatively constant speed. With the reasoning I give below Feynman...
  46. Hak

    I How Does Special Relativity Affect Perceptions of Simultaneity?

    I have always had certain difficulties in correctly understanding the theory of special relativity; I often apply it to certain situations and they fall apart... Imagine there is a rectangular object placed with its long sides parallel to the ground and its short sides perpendicular to it...
  47. Feynstein100

    I Using GR to predict the shape of the entire universe?

    So I've often heard that when GR is applied to the entire observable universe to calculate its curvature, we get a value of zero, meaning that the entire universe is flat. I've got 2 problems with this. The first is that I thought GR was a local theory i.e. it only applies locally. Trying to...
  48. Z

    I How many meter sticks are there in this length contraction reasoning?

    I have a question about the concept of length contraction. The black line from (0, 0) to (1, 0) represents a meter stick in my stationary frame, call it frame A. The blue axes represent my coordinate system with coordinates x and t. The green axes represent the coordinate system of a moving...
  49. D

    I Suggestion for 2 more GR tests

    Although there are tons of experimental tests/confirmations for General Relativity, I noticed that most of them are made on/from Earth, or very close to Earth, so in this thread I'll suggest 2 extensions of past experiments: 1. GSM GPS satellite (preferably with an unmodified atomic clock) far...
  50. A

    I A question about static spacetime in GR

    Hello, I'm studying General Relativity using Ray D'Inverno's book. [Moderator's note: link deleted due to possible copyright issues.] . I don't understand what the author writes in paragraph 14.3 ("Static solutions") where he demonstrates that for a static spacetime there are no cross-terms...
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