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
Recent contents Top users
  1. K

    I What Happens Inside BH Event Horizon?

    I have read about the spaghettification of objects due to tidal forces as they get close to the singularity. Gravity at your feet is stronger than at your head, so you get stretched and pulled apart. In this case, the singularity is a point in space. But I also read about the time coordinate...
  2. ohwilleke

    A LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena

    A new group of investigators are attempting something similar to Deur's work, which seeks to explain dark matter phenomena with general relativity corrections to Newtonian gravity is systems like galaxies. Deur's most similar publication to this one along these lines was: One thing that makes...
  3. kirkr

    A Schwarzschild Geometry: Evaluating Proper Distance

    Schwarzschild Geometry-proper distance. From what I have studied when the Schwarzschild line element is evaluated at constant time and at a constant radius , proper distance becomes a Euclidean distance on the surface of a sphere. What I don't understand is how to evaluate the integral...
  4. Adwit

    From General Relativity to Dark Energy

    If we insert the values from (2.9), (2.10), (2.11) into (2.5) & (2.6) how can we get (2.13) & (2.14) ?? I need to see the calculations step by step.
  5. lindberg

    I Can Shape Dynamics Be Tested Against Quantum Mechanics?

    Shape Dynamics implements nicely Mach's principles. But how well does it fare when it comes to Quantum Mechanics? How can it be experimentally distinguished from other theories?
  6. Spockishere

    I Infinite Frequencies & Extraterrestrial Signals: What Are We Missing?

    And if there are an infinite amount of frequencies, doesn't that mean that an extraterrestrial civilization could be reaching out without us being able to receive their signals. And even if we did receive their signals, how would we understand their form of communication? What if they...
  7. D

    B General Relativity & Ether: Clarifying a Contradiction?

    Hope this question can be quickly clarified: There was a statement that the General Relativity can be interpreted by speaking of an ether whose state varies from point to point. Is this correct?!
  8. LCSphysicist

    Relativity General relativity with focus on action?

    I am having a class of general relativity. It seems that the professor will follow an approach which consist of achieve the action, and variate it to get the equations of motion (indeed, that's how we already got the geodesic equation, the dynamics of a particle in electromagnetism, the equation...
  9. Z

    I GR: Practical Problem Sets w/ Solutions

    I have been learning gr on YouTube for the last few months. Most of the videos and the book I have focus on high level understanding. I can do all of the tensor calculus proofs. However simple questions like how you set up a velocity vector or measure proper time in schwarzschild are beyond me...
  10. physicsuniverse02

    Does anyone know which are Ricci and Riemann Tensors of FRW metric?

    I just need to compare my results of the Ricci and Riemann Tensors of FRW metric, but only considering the spatial coordinates.
  11. A

    I Ideal Fluids & General Relativity: Why Needed?

    Why in general relativity do we need the physics of perfect fluids?
  12. A

    I General Relativity: Is it Local?

    Spacetime is a differential manifold and at each point is attached a Minkowski spacetime. There the laws of physics are the usual ones without gravity. Gravity is the curvature of spacetime. To define the concept of curvature do we need to evaluate at least one neighborhood of point P? Is...
  13. C

    B Robert Wald's General Relativity: Energy-Momentum Relation

    Hello, this is my first thread. Robert Wald, in General Relativity, equation (4.2.8) says : E = – pa va where E is the energy of a particle, pa the energy-momentum 4-vector and va the 4-velocity of the particle. How can I see this is compatible with the common energy-momentum-relation E2 – p2 =...
  14. K

    I Length contraction in General Relativity

    In GR, a free falling object when viewed by a distant observer appears to be length contracted and slows down as it approaches the event horizon of a black hole. The length contraction piece, however, seems counterintuitive. I would have thought that the leading edge of the object would...
  15. S

    A Does Spacetime Absorb Energy in General Relativity?

    Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way. However, many other...
  16. A

    Mathematical prerequisites for general relativity

    What mathematical topics do I need to know to start studying general relativity? From which textbooks can I learn them? I don't currently know anything about differential geometry. I know calculus, linear algebra, mathematical methods of physics (the necessary topics for quantum mechanics) and...
  17. Tertius

    A Local phase invariance of complex scalar field in curved spacetime

    I am stuck deriving the gauge field produced in curved spacetime for a complex scalar field. If the underlying spacetime changes, I would assume it would change the normal Lagrangian and the gauge field in the same way, so at first guess I would say the gauge field remains unchanged. If there...
  18. BiGyElLoWhAt

    I A couple questions about the Riemann Tensor, definition and convention

    According to Wikipedia, the definition of the Riemann Tensor can be taken as ##R^{\rho}_{\sigma \mu \nu} = dx^{\rho}[\nabla_{\mu},\nabla_{\nu}]\partial_{\sigma}##. Note that I dropped the Lie Bracket term and used the commutator since I'm looking at calculating this w.r.t. the basis. I...
  19. G

    B General Relativity: Action & Reaction in Gravitation

    Hi, In general relativity, gravitation is not anymore a Force but a deformation of space time. I would like to know what's becomes the 3 law of Newton for gravity that action equal reaction ? When a apple fall on the earth, does "the force" is exactly the same as the one applied on Earth ...
  20. Jamestein Newton

    I Discussing General Relativity - Beliefs & Ideas

    Following are not strictly physics questions. But cool questions to discuss. We need to add dark energy to our cosmological model if we strictly follow GR. This lead to some beliefs that GR is an effective theory. (1)Do you believe that GR is the fundamental theory? If GR is an effective...
  21. Aerodyn

    I Understanding Gravity with GR: Beginner's Guide by Aerodyn

    Hi everybody. I recently started to learn GR from a very begginer level. I would like to share with you some lines of discussion, to understand your approach to some specific topics which for me are key to better understand the whole story. If a put an accelerometer on the floor it reads 9.8...
  22. Sciencemaster

    I Adapting Schwarzschild Metric for Nonzero Λ

    So, there are a fair amount of metrics designed with a zero value for the cosmological constant in mind. I was wondering if there was some method to modify metrics to account for a nonzero cosmological constant. Say, for instance, the Schwarzschild metric due to its relative simplicity. A...
  23. Tertius

    I Computing Volume in General Relativity: Use of Tensor & Friedmann Eqns

    When we compute the stress energy momentum tensor ## T_{\mu\nu} ##, it has units of energy density. If, therefore, we know the total energy ##E## of the system described by ## T_{\mu\nu} ##, can we compute the volume of the system from ## V = E/T_{00}##? If it holds, I would assume this would...
  24. phyz2

    I Klein Gordon Invariance in General Relativity

    Hello! I'm starting to study curved QFT and am slightly confused about the invariance of the Klein Gordon Lagrangian under a linear diffeomorphism. This is $$L=\sqrt{-g}\left(g^{\mu\nu}\partial_\mu \phi \partial_\nu \phi-\frac{m^2}{2}\phi^2\right),$$ I don't see how ##g^{\mu\nu}\to...
  25. mollwollfumble

    I Has anyone done a PPN formalism on Dark Matter? Or other non-GR?

    This thought surprisingly came from thinking about the definition of temperature and the symmetry breaking that separated time from temperature. Which led to thoughts about symmetry breaking that separated QM from GR. Which led to to the symmetry breaking that separated dark energy from baryonic...
  26. G

    A Understand (k,l) Tensors in Gen. Relativity

    In both Wald and Carroll, a type (k,l) tensor has k dual vectors and l vectors, yet a (1,0) tensor is a vector and a (0,1) tensor is a dual vector. I must be missing something simple. Please explain.
  27. R

    I Black Hole Waterfall Analogy & Light Speed

    Recently I have seen a number of General Relativity visualisations that show spacetime flowing towards any mass, similar to water flowing into a sink hole. ScienceClic's video is an example. That model is also used in the "waterfall model" to explain the event horizon of a black hole, as the...
  28. E

    A Can Einstein Tensor be the Product of Two 4-Vectors?

    In Gravitation by Misner, Thorne and Wheeler (p.139), stress-energy tensor for a single type of particles with uniform mass m and uniform momentum p (and E = p2 +m2) ½ ) can be written as a product of two 4-vectors,T(E,p) = (E,p)×(E,p)/[V(E2 – p2 )½ ] Since Einstein equation is G = 8πGT, I am...
  29. Question69

    B Is energy really not conserved in a constantly expanding Universe?

    Is energy really not conserved in a constantly expanding universe?
  30. The Bill

    Relativity Opinions on Rovelli's General Relativity: The Essentials?

    I recently noticed that "General Relativity: The Essentials" by Carlo Rovelli has been published. Based on the description, table of contents, and the Amazon reviews, it seems to me that it might be a spiritual successor to Dirac's "General Theory of Relativity." Is that an accurate assessment...
  31. T

    A Covariant Derivative of Stress Energy Tensor of Scalar Field on Shell

    Hi all, I am currently trying to prove formula 21 from the attached paper. My work is as follows: If anyone can point out where I went wrong I would greatly appreciate it! Thanks.
  32. Pyter

    I What's the underlying frame of the Einstein's Field Equation?

    Hello all, I have a question on a pivotal concept of GR that I've never managed to fully grasp. In what coordinate system is the Einstein's Field Equation set up and solved? I've always assumed it's an Euclidean 4D space, whose metric is irrelevant because we are dealing with scalar...
  33. Alpha2021

    A General Relativity: Section 5.1 Homogeneity & Isotropy Analysis

    From the section[5.1] of 'Homogeneity and Isotropy' from General Relativity by Robert M. Wald (pages 91-92, edition 1984) whatever I have understood is that - ##\Sigma_t## is a spacelike hypersurface for some fixed time ##t##. The hypersurface is homogeneous. The metric of whole space is ##g##...
  34. sophiatev

    A Characterizing GR Traj in Minkowski Space

    In Minkowski space, with line element $$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$$ (and ##c = 1##) we take spacelike trajectories to have ##ds^2 > 0##, null trajectories to have ##ds^2 = 0##, and timelike trajectories to have ##ds^2 < 0##. This makes sense given our definition of the line element...
  35. Y

    A B and A in Curved Space Time: Does \nabla \times A =B?

    By definition of the vector potential we may write \nabla \times A =B at least in flat space. Does this relation hold in curved space? I am particularly interested if we can still write this in a spatially flat Friedmann-Robertson-Walker background with metric ds^2=dt^2-a^2(dx^2+dy^2+dz^2) and...
  36. S

    I Time Dilation at Moving Black Hole Event Horizon

    Hello everyone, I have a hard time to conceptualize the case of a moving black hole. We know from SR that time slows down for moving objects; but time dilation at the event horizon is already equal (tends) to zero. It seems that it can create some sort of conflict for the black hole movement...
  37. P

    A Why are General relativity texts so much more formal?

    Hi all, What I notice is that there's a significant difference in style between the GR texts and the other textbooks. In particular, GR texts very much try hard to read like a math textbooks, emphasizing theorems and abstract definitions, which I'm not sure are practically useful (though...
  38. C

    Space-like trajectory in Schwarzschild spacetime

    I'm not sure how to approach this question. So I start off with the fact the path taken is space-like, $$ds^2>0$$ Input the Schwarzschild metric, $$−(1−\frac{2GM}{r})dt^2+(1−\frac{2GM}{r})^{−1}dr^2>0$$ Where I assume the mass doesn't move in angular direction. How should I continue?
  39. BadgerBadger92

    Relativity Good Beginner's General Relativity Books?

    I want to learn General Relativity so I am looking for a good beginners book with low amounts of math and clear explanations. Any suggestions?
  40. Z

    I Do Fictitious Forces Still Matter in General Relativity?

    hello it is well known that gravitationl force is actually a fictitious force generally speaking,are fictitious forces still necessary in general relativity ? the fictitious forces which we experience on a bus or on a car can also be understood as due to the spacetime distortion ?
  41. E

    Who is Edward G. Timoshenko, PhD in theoretical physics?

    Edward G. Timoshenko PhD, MSc, EurPhys, CPhys MInstP, CChem MRSC Web site: https://www.EdTim.live Bio: 2011- Researcher, TEdQz Research after an early retirement from UCD 2005 - 2011 Senior Lecturer in Physical Chemistry, School of Chemistry and Chemical Biology, UCD 1997 College Lecturer...
  42. U

    Help in derivation of Birkhoff's theorem

    Using the transformation for ##t##, I obtained $$\mathrm{d}t'=\left(1+\frac{\partial f}{\partial t}\right)\mathrm{d}t+\frac{\partial f}{\partial r}\mathrm{d}r$$. Using this equation, I substituted it into the general line element to obtain \begin{align*}...
  43. ergospherical

    Relativity "Must-read" papers in general relativity

    I found an interesting list of "must-read" papers in the field of general relativity compiled by Emanuele Berti: https://pages.jh.edu/eberti2/posts/must-read-paper-list/ Are there any notable exceptions, or other "classic" papers that - in your view - every relativist ought to have read?
  44. Sciencemaster

    I Piecewise Functions in the Einstein Field Equations

    Let's say I want to describe a massive box in spacetime as described by the Einstein Field Equations. If one were to construct a metric in cartesian coordinates from the Minkowski metric, would it be reasonable to use a piecewise Stress-Energy Tensor to find our metric? (For example, having...
  45. cianfa72

    I Detecting Gravitational Waves w/ Interferometers: Explained

    Hi, I would like to ask for some clarification about the physics involved in the gravitational waves detection using interferometers. Starting from this thread Light speed and the LIGO experiment I'm aware of the two ends of an arm of the interferometer (e.g. LIGO) can be taken as the...
  46. N

    I Hafele-Keating Exp: Balancing SR Effects in Plane Ref Frame

    I have seen the "Hafele-Keating with the plane as reference frame?" thread (https://www.physicsforums.com/threads/hafele-keating-with-the-plane-as-reference-frame.767913/ ), but the replies do not seem to explain (to me anyway) what when taking a plane as a reference frame, balances the slowing...
  47. joneall

    A Understanding Frame Fields in GR: A Beginner's Guide

    I'm having trouble with Rovelli's new book, partly because the info in it is pretty condensed, but also because his subjects are often very different from those in other books on GR like the one by Schutz. For one thing, he never uses the term "manifold", but talks about frame fields, which seem...
  48. Thytanium

    A Radial Excess Calc: GR, 4πGρ & R00

    Which is the mathematical procedure to obtain ##\delta r = \frac{GM}{3c^2}## from ##\nabla^2 V = R_{00} = 4\pi G\rho## where ##\nabla^2 V## is volume contraction of a spherical mass of density ##\rho## and ##R_{00}## is the 00 component of Ricci tensor ##R_{ij}##?
  49. S

    B Time Dilation in a Galaxy: Calculating Mass Effects

    Hello everyone - The gravitational force near the edge of the galaxy at point A (see attached image) can be calculated by assuming that all the galactic mass is located in the center of the galaxy. - In order to calculate the gravitational force in the middle of the galaxy (point B) we take...
  50. Amaterasu21

    B Charged Particle on Earth's Surface: Will It Emit Radiation?

    General relativity tells us that an object in free-fall is actually inertial, following a geodesic through curved spacetime, and not accelerating. Instead, it's objects like us, on the surface of a large body, that are accelerating upwards. Maxwell's equations also tell us that accelerated...
Back
Top