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

    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...
  2. 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?
  3. J

    Relativity Callahan's "The Geometry of Spacetime"

    Hello, I was wondering if anyone knows about the the book "The Geometry of Spacetime: An Introduction to Special and General Relativity" by Callahan and what their opinions are. Thanks!
  4. J

    Relativity Differential Forms and the Geometry of General Relativity

    Hello, I would like to know if anybody here has used the book "Differential Forms and the Geometry of General Relativity" by Tevian Dray and how they found it. Thanks!
  5. redtree

    A Weyl Vacua Solutions to GR: Derivation from Riemann Tensor

    Where can I find a derivation of the vacuum solution for GR directly from the Riemann tensor of zero trace, i.e., Weyl tensor, instead of the more traditional Schwarzschild derivation?
  6. F

    I Is gravity really not a force according to the weak equivalence principle?

    From the weak EP, inertial mass is equivalent to the gravitational mass. The weak EP implies the universality of gravitation. Some implications of the EP are: 1) Gravity is inescapable - there is no such thing as gravitationally neutral object with respect to which we can measure the...
  7. A

    Relativity Free PDF download of Hawking & Ellis (1973)

    Where can I find a free digital copy of The Large Scale Structure of Space-time by Hawking and Ellis?
  8. F

    A Manifolds: local & global coordinate charts

    I'm fairly new to differential geometry (learning with a view to understanding general relativity at a deeper level) and hoping I can clear up some questions I have about coordinate charts on manifolds. Is the reason why one can't construct global coordinate charts on manifolds in general...
  9. F

    A What is a topology intuitively?

    I've recently been studying a bit of differential geometry in the hope of gaining a deeper understanding of the mathematics of general relativity (GR). I have come across the notion of a topology and whilst I understand the mathematical definition (in terms of endowing a set of points with the...
  10. G

    I Need for GR: Historical Indications

    Hi. There were theoretical (find transformations under which Maxwell's equations remain invariant) and experimental (speed of light is constant, Michelson-Morley) indications that made the development of SR inevitable. But what about GR? Was there a "need" for this theory or was Einstein just...
  11. willem govaerts

    I Did the Big Bang separate space and time

    Hello everyone, I've come across a problem that i can't solve but which i find really interesting. I'm not here to ask where the big bang was because I've already read enough about that is was a singularity, so you could say that is was everywhere. But here my problem comes in, if the big bang...
  12. t_r_theta_phi

    I Metric for Infinite Rod in Gen. Relativity

    What is the metric for the spacetime around an infinitely thin, infinitely long, uniform rod? Could it be written in the form ds2 = A(r)dt2 + B(r)dr2 + C(r)dh2 + r2dθ2 where h is the coordinate along the rod and r is the radial coordinate, or would it be something more complicated?
  13. Daleri Mc Rileda

    B How Far Is It To The Center Of The Milky Way/Tootsie Pop?

    With length contraction being ever increased while approaching the mass of a black hole singularity, how does one measure the distance to the virtual infinite contracting frames of reference of time and space /distance of the singularity? Related question : How can one measure the size of a...
  14. J

    Relativity Opinions on Zee's "Einstein Gravity in a Nutshell"

    Hello again, I would like to know what your opinions about this book. As I have figured out, there are a lot of great GR books out there, but this very rarely gets any mention in forums like this. Why is this? Its got pretty good reviews at amazon and goodreads. Thanks in advance!
  15. J

    Relativity On Sean Carroll's General Relativity textbook

    I have heard/read that Carroll's Spacetime and Geometry: An Introduction to General Relativity is one of the best books on General Relativity but its price is insanely high! Does anybody know any place which sells it at a lower price than, say, Amazon? If not, what are other books that cover...
  16. DuckAmuck

    I Black Holes and Charged Particles

    What happens when charged particles fall into a black hole? Say like N electrons fall in, giving the black hole a net charge of -N. Since light cannot escape the event horizon, I imagine electric fields cannot either, since they are mediated by photons. So is that charge effectively lost until...
  17. mertcan

    A Stress energy tensor general relativity

    Hi, I would like say that in this link ( ) and starting from 56.28 Suskind tries to find the energy tensor equation using \phi, afterwards he finds a equation similar to wave equation in terms of \phi. My question is: For what does \phi stand ? I could not capture the meaning of \phi. Could...
  18. A

    A Metric with Harmonic Coefficient and General Relativity

    Goodmorning everyone, is there any implies to use in general relativity a metric whose coefficients are harmonic functions? For example in (1+1)-dimensions, is there any implies for using a metric ds2=E(du2+dv2) with E a harmonic function? In (1+1)-dimensions is well-know that the Einstein...
  19. A

    I Understanding General Relativity

    I am reading general and special relativity from a book and I am stuck with these lines please can someone provide its detailed explanation "Einstein demanded that the special principle of relativity should be valid also for Maxwell’s electromagnetic theory. This was obtained by replacing the...
  20. E

    I Meaning of the equivalence principle in General relativity

    It is known that equivalence principle is good for understaning of general relativity (GR). This means comparison of the elevator and falling in homogenic gravitational field. But, I here somewhere something like "in the higher lever of GR, let us forget on principle of equivalence". How it is...
  21. PabloAMC

    A Problems between Quantum Mechanics and General Relativity

    I have read several times that general relativity has some problems with quantum mechanics and they are not compatible. However, special relativity can be introduced in quantum mechanics mainly by Dirac equations (so I am pretty sure that the problem of passing from a frame where the parameter...
  22. S

    Relativity What Are Good Beginner Books on General Relativity with Mathematics?

    HI, can anyone suggest a good book on general relativity with fairly good mathematics for beginner for self study?
  23. L

    I Galilean Equivalence Principle: Extended Objects

    The Galilean equivalence principle (or weak equivalence principle) is the statement of the universality of free-fall under gravity. For example, according to Wikipedia, it can be stated as follows My question regards the limitation of the principle to point masses. Does universality of...
  24. K

    I Fixed Stars Moving Faster Than Light? Problem?

    If I spin around in an open field at night and look up to the stars they appear to be moving relative to me. Additionally, they are very far away and trace out a giant arc length in a very short time (S=rθ). With respect to me, these stars are moving faster than light. Is this a problem? Has...
  25. myra2016

    Find Null Geodesics with affine parameter

    Homework Statement The metric is given by https://dl.dropboxusercontent.com/u/86990331/metric12334.jpg H is constant; s is an affine parameter, and so r(0)=t(0)=0. Apologise in advance because I'm not very good with LaTex. So I used Word for equations, and upload handwritten attempt at...
  26. G

    I Raising index on covariant derivative operator?

    In Carroll, the author states: \nabla^{\mu}R_{\rho\mu}=\frac{1}{2} \nabla_{\rho}R and he says "notice that, unlike the partial derivative, it makes sense to raise an index on the covariant derivative, due to metric compatibility." I'm not seeing this very clearly :s What's the reasoning...
  27. pitbull

    Bachelor's thesis about Gravitational Waves -- Too advanced?

    Hey! I am about to start my Bachelor's thesis about General Relativity. My professor mentioned that my thesis might as well be related to Gravitational Waves. Do you think that it would be appropriate to work on Gravitational Waves for a Bachelor's thesis? Isn't it too advanced? Also, any idea...
  28. G

    I GR vs SR: Is a Connection Necessary?

    Hi, When I started learning about GR I wondered if it emerged from SR (which the name suggests) or if the connection between the two is mere technical. GR describes the behaviour of the metric of space-time, which is locally Minkowskian and therefore SR applies. But is a curvature-based theory...
  29. philipp

    I Time dilation in special vs. general relativity

    Hi all, I was trying to understand the time dilation in special and general relativity and after much time of "overthinking" I am pretty much stuck now. My problem is, that what seems to me to be the same premises apparently imply opposite things. In special relativity, for two inertial...
  30. L

    Cosmology Cosmology&particles astrophysics textbook

    Could you recommend me some good textbooks on cosmology, please? I'm looking for something that covers both general relativity topics and, which is more important for me, particles astrophysics stuff. I like the structure of Bergström&Goobar's book but it's a little bit sketchy. Something with...
  31. W

    Riemann tensor given the space/metric

    Homework Statement Given two spaces described by ##ds^2 = (1+u^2)du^2 + (1+4v^2)dv^2 + 2(2v-u)dudv## ##ds^2 = (1+u^2)du^2 + (1+2v^2)dv^2 + 2(2v-u)dudv## Calculate the Riemann tensor Homework Equations Given the metric and expanding it ##~~~g_{τμ} = η_{τμ} + B_{τμ,λσ}x^λx^σ + ...## We have...
  32. W

    Covariant derivative of vector fields on the sphere

    Homework Statement Given two vector fields ##W_ρ## and ##U^ρ## on the sphere (with ρ = θ, φ), calculate ##D_v W_ρ## and ##D_v U^ρ##. As a small check, show that ##(D_v W_ρ)U^ρ + W_ρ(D_v U^ρ) = ∂_v(W_ρU^ρ)## Homework Equations ##D_vW_ρ = ∂_vW_ρ - \Gamma_{vρ}^σ W_σ## ##D_vU^ρ = ∂_vU^ρ +...
  33. G

    A Mapping Tangent Space to Manifold - Questions & Answers

    Hi all, this might be a silly question, but I was curious. In Carroll's book, the author says that, in a manifold M , for any vector k in the tangent space T_p at a point p\in M , we can find a path x^{\mu}(\lambda) that passes through p which corresponds to the geodesic for that...
  34. Augbrah

    Projecting push forward of a vector

    Homework Statement Say we have two manifolds N(dim d) and M(dim d-1). Let Φ: M →N be a diffeomorphism where Σ = Φ[M] is hypersurface in N. Let n be unit normal field (say timelike) on Σ and ⊥ projector (in N) defined by: ⊥^a_b = \delta^a_b + n^a n_b Where acting on (s, 0) tensor projection...
  35. Augbrah

    Show that killing vector field satisfies....

    I'm trying to do past exam papers in GR but there are some things I don't yet feel comfortable with, so even though I can do some parts of the question I would be very happy if you could check my solution. Thank you! 1. Homework Statement Spacetime is stationary := there exists a coord chart...
  36. Z

    I Gravitational Constant in GR: How & Why?

    (precursor: I have not formally studied GR) I have noticed that the gravitational constant found in classical gravitation is also used in GR. Why is this the case? Am I correct in thinking that the constant was determined by Cavendish and was for the classical theory of gravitation? So, my...
  37. A

    A How do we say that the universe we live is 3 dimensional?

    i opine that the universe is not 3 dimensional at all. its not build up of 3 coordinates at all. it is because, we humans could see 3 dimensions it doesn't mean the space metric is of 3 dimensions. suppose there's a super being living on an Earth like planet of some other galaxy whose viewing...
  38. Cosmology2015

    I Energy Locally Never Negative: Explained

    Hello to all members! I heard on a documentary about general relativity and singularities that "energy is locally never negative". However, I was not able to get grasp the meaning of this term. Could someone explain to me the meaning of this term in the framework of general relativity. I really...
  39. Devin

    I Production of Gravitational Waves Problem: Energy Flux

    Suppose two masses are connected via a really strong spring, where one of the masses undergo an acceleration towards a relativistic speed, by say a rocket that leaves the scene soon after. When in isolation, (the two masses), they exhibit a sinusoidal oscillation to and fro. What is the...
  40. J

    A Covariant derivative definition in Wald

    I'm working through Wald's "General Relativity" right now. My questions are actually about the math, but I figure that a few of you that frequent this part of the forums may have read this book and so will be in a good position to answer my questions. I have two questions: 1) Wald first defines...
  41. P

    B Is the Universe discrete or continuous?

    Apologies if this question has been asked already. I've been given resources to help me understand, but it's been hard for me to wrap my head around the answer and, for that matter, it is difficult to understand a text when you have to look up every other word (an exaggeration, but you know ...
  42. T

    I Event Horizon of Telescope Through Earth: Does It Exist?

    Assume we drill a hole through the Earth - through the center towards the other side. Then we use a telescope, point it through the hole and observe stars on the other side of the earth. The telescope experiences a constant acceleration from Earth's gravitation. Accelerated movements have an...
  43. EnumaElish

    I (How) does the LIGO experiment falsify Newtonian gravity?

    Sorry for the amateurish setup that follows. Here's my thought experiment. Consider a 2-dimensional universe on the Cartesian plane. Earth is located at point (0,0). There is a binary system {A,B} oscillating around (1,1). To simplify, assume that the oscillation is 1-dimensional and occurs on...
  44. L

    Other Undergraduate research on gravitational waves

    Currently I'm in the last year of the Physics course and I'm interested in working on some undergraduate research project. At first I was suggested to work with statistical physics, but I believe I would prefer working with General Relativity. From the point of view of background I do have a...
  45. L

    I Exploring General Relativity: A Beginner's Guide

    What is general relativity all about. I don't know anything about it. I am an undergrad.
  46. davidbenari

    I Understanding 4-Momentum in General Relativity

    Conserved quantities in GR deal with ##p_\mu## not ##p^\mu## and while in Minkowski spacetime its easy to see what each of the components mean (since the metric is so simple) in general relativity I think its not and its starting to confuse me. Why exactly is ##-p_0## the energy in general...
  47. H

    I Density Curvature Parameter: Can We Predict?

    If I know the density curvature parameter for today $$ \Omega_{k,0} = \frac{-c^{2}k}{R_{0}H_{0}} $$ then is it possible to surmise what it would be, say, during the matter dominated era $$ \Omega_{k,t} = \frac{-c^{2}k}{R(t)H(t)}$$ ?
  48. C

    A Metric of n-sheeted AdS_3: Constructing BTZ

    suppose the AdS_3 metric is given by $$ds^2 =d\rho^2+cosh^2\rho d\psi^2 +sinh^2 \rho d\phi^2$$ what is the n-sheeted space of it? Can the n-sheeted BTZ be constructed from it by identifications as n=1 case? Thanks in advance.
  49. D

    I Newtonian limit of Schwarzschild metric

    If I am asked to show that the tt-component of the Einstein equation for the static metric ##ds^2 = (1-2\phi(r)) dt^2 - (1+2\phi(r)) dr^2 - r^2(d\theta^2 + sin^2(\theta) d\phi^2)##, where ##|\phi(r)| \ll1## reduces to the Newton's equation, what exactly am I supposed to prove?
  50. J

    Geometry Book on Differential Geometry/Topology with applications

    Hello! I want to learn about the mathematics of General Relativity, about Topology and Differential Geometry in general. I am looking for a book that has applications in physics. But, most importantly, i want a book that offers geometrical intuition(graphs and illustrations are a huge plus) but...
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