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.
I don't know much about general relativity, but I'm curious if Zeno somehow foresaw the reallty of the universe many many years before Einstein did(without any rigour ofc, but still the idea holds?).
Understanding the Zeno's arrow paradox, stating that an arrow is motionless at a certain moment...
If general relativity in the formal sense constrains all velocities to the speed of light as a maximum, how would superluminal group velocities exceeding speeds of light (at their superpositions) be evaluated in mainstream physics? Would this be a case of General Relativity and Physics...
In the context of General Relativity spacetime is a four-dimensional Lorentzian manifold M with metric tensor g, its Levi-Civita connection \nabla and a time orientation vector field T \in \Gamma(TM).
In this context I've seem the following three definitions:
A coordinate system is a chart...
I just started reading general theory of relativity. I have some elementary questions. Not an english speaker so bear with me.
I am reading the thought experiment which describes path of a photon in a free falling lift. For an observer inside the lift, the photon path is a straight line. But...
How do I calculate the gravitational mass of a cylinder of compressed gas, including the effects of pressure? By gravitational mass, I mean what I would measure on an ideal mass balance.
(I know that the pressure is negligibly small in a realistic container, but I want to have a conceptual...
Have members of the community had the experience of being taught GR both from a mathematical and physics perspective?
I am a trained mathematician ( whatever that means - I still struggle with integral equations :) ) but I have always been drawn to applied mathematical physics subjects and much...
This isn't homework, nor is it an exercise problem; merely a question about a diagram.
Re: B.Schutz book "A First Course in General Relativity" 2nd Edition, (Asian print version), page 5, Figure 1.1 "A spacetime diagram in natural units".
From section 1.4 Spacetime diagrams:
A world line is...
Hello there, I've been considering the geodesic equations of motion for a test particle in Schwarzschild geometry for some time now. Similar to what we can do with the Kepler problem I would like to be able to numerically integrate the equations of motion. I'm quite interested to see how...
First I don't have extensive knowledge about gravity beyond General Relativity, so please forgive my ignorance about this subject. I have confusion about the relation between GR and QM and I just want a general picture so that I can connect the dots.
My questions:
1- Why do we need quantum...
As per the above figure coil A is situated inside a magnetic field caused by small accelerating objects B which in turn are causing the larmor frequency in coil
Object C or train of objects C have quadruple movement and are rotating around the coil A giving out gravitational waves.
Objects C...
Hello everyone, here I come with a question about inertial frames as defined in General Relativity, and how to prove that the general definition is consistent with the particular case of Special Relativity.
So to contextualize, I have found that one can define inertial frames in General...
Ignoring for the moment the plausibility of this scenario, what would happen? A black hole is the ultimate gravity well, right? In some circles, they're even considered tears in the fabric of the universe. So what would happen to that fabric if you moved the black hole?
Would it behave like...
I desire to read General relativity by Wald. I am a student who is self teaching, and I know tensor calculus by Pavel grinfield's introduction to tensor analysis and calculus of moving objects. The book states things from advanced calculus. Do I have more math to learn before hand?
It is commonly said that if you lift an object above the Earth it gains potential
energy equal to mgh (m=mass, g=gravitational acceleration, h=height), suggesting
that the potential energy is in the lifted mass.
This cannot be. Consider the case of two perfectly rigid spheres, isolated in...
Is the Hubble's law(recessional velocity linearly proportional to distance) valid for all cases even when the spacetime is curved? Is there a nonlinear model for Friedman models or it's always linearly proportional?
Classical mechanics: a minimal standard course by Sergei Winitzki. It is not probably going to help you if you already did not know the subject but is a great refresher nonetheless. He also includes a differential equations refresher that I found invaluable.
Looks like he has a ton of other...
Dear All,
I am trying to find some good books that provide a comprehensive one-stop education for special and general relativity, with concise coverage of key fundamentals of the maths involved.
It is intended for self study, and I do not have strong fundamentals on advanced physics / maths...
Homework Statement
I want to calculate the on shell action for the case of a AdS Schwarzschild black hole.
Homework Equations
Following the case of the flat Schwarzschild black hole I tried to add a counter-term of the type of a Gibbons-Hawking boundary term for flat Minkowski spacetime...
Has anyone heard of "Bauer's Paradox" in Einstein's working out his equations for General Relativity? The description I came across was extremely fuzzy (something about an expression for a certain tensor adding up to be zero when it shouldn't, or vice-versa), so I am looking for a better...
I am thinking about taking GR as an elective,but I have no plans on going into cosmology or any related field.I wanted to know if when applying for graduate school,whether it is a positive for them to see you have taken a "high level" course,such as GR.
I know that the best thing is to have...
Let us assume that a spacetime has a global time-displacement symmetry described by a timelike Killing vector field ##\xi^\mu=(1,0,0,0)##.
Further assume that we have a particle with four-momentum ##P^\mu=m\ V^\mu##.
It is well-known that a stationary observer with four-velocity ##U^\mu##...
I've been studying a bit of differential geometry in order to try and gain a deeper understanding of the mathematics of general relativity (GR). As you may guess from this, I am approaching this subject from a physicist's perspective so I apologise in advance for any lack of rigour.
As I...
Last year I finished the undergraduate course in Mathematical Physics. This year, more precisely in March, I'm going to start the graduate course to acquire a master's degree in Physics.
Now, for this course I must choose a research topic and find an advisor. This is being a little bit...
I have seen the derivation for Unruh radiation for a massless, non-interacting scalar field (Carroll). Are there interesting differences that arise for more realistic standard model cases. For example, what does QCD look like for an accelerating observer? Any papers that detail this would be...
Why is i that two cones connected at their vertices is not a manifold? I know that it has to do with the intersection point, but I don't know why. At that point, the manifold should look like R or R2?
Homework Statement
I have ##R^{u}_{o b u } F^{o}_a - R^{u}_{oau}F^{o}_{b}##
and I want to show that this equal to ##2R_{o[aF^{o}_b]}##
where ## [ ] ## denotes antisymmetrization , and ##F_{uv} ## is a anitymstric tensor
Homework Equations
Since ##F_{uv} ##is antisymetric the...
As far as I can tell, in GR, the Chirstoffel symbol in the expression of the Connection is analogous to the vector potential, A, in the definition of the Covariant Derivative.
The Chirstoffel symbol compensates for changes in curvature and helps define what it means for a tensor to remain...
Homework Statement
Calculate the circumference of the circle θ = θ0 (a constant) in the spatial geometry
\begin{eqnarray*}
dS^2 = a^2(d\theta^2 + sin^2\theta cos^2\theta d\phi^2)
\end{eqnarray*}
Hence, (by finding R(z)) sketch the cross section of the surface embedded in three dimensions via...
Homework Statement
A stationary, axisymmetric, spacetime has two Killing vector fields [ξt, ξφ] corresponding to translation along t or φ directions. A particle of unit mass moving in this spacetime has a four-velocity u = γ[ξt + Ωξφ].
(i) Explain why we can interpret this as a particle moving...
Hello, does anyone know if a solution to EFEs (Einstein's Field Equations) has been found that's analogous to Helmholtz's vortex ring solutions in fluid dynamics?
I am trying to find a derivation of gravitational redshift from a static metric that does not depend on the equivalence principle and is not a heuristic Newtonian derivation. Any suggestions?
I have a few conceptual issues following a standard thought experiment to argue why light bends in a gravitational field and I'm hoping I can clear them up here.
Consider an observer in a lift in free-fall in a uniform gravitational field and an observer at rest in the uniform gravitational...
Is it correct, at least in the context of general relativity, to say that in a coordinate basis, the inner product between space-like basis vectors will be 1, and in a non-coordinate basis the inner product will be defined by the corresponding component of the metric? Can I take this conditions...
Is there a formulation of any of the relativity theories in terms of complex analysis? As in - I imagine - every event would be a complex number in a complex field.. or something as such..
I understand that General Relativity can make a difference between a spinning and non spinning mass thus can make better prediction for planetary orbits for example. The effect is frame dragging.
However if we simulate a Newtonian gravitation and instead of representing a planet as a sphere...
In my Google searchs and by reading threads on this forum I've seen that the books people most recommend on general relativity are
Graviation, by Thorne, Wheeler and Misner,
Wald's book and
Weinberg's book.
I'm in the first year to get a bachelor degree on physics and I could read any of these...
I've heard that unlike Special Relativity, General Relativity claims that you can' say any reference frame is better than another frame, including frames in which Newton's Laws don't hold. I've seen debates about this specifically in the context of geo/helio-centrism. From what I understand...
I have to do a project on wormholes as solutions to the EFE, but I'm only and undergrad and have not yet taken any GR classes. I found a paper by Michael Morris and Kip Thorne with a derivation of a simple wormhole (many assumptions), but because of my lack of experience I can't tell what the...
Hi. (I'm sorry for my poor English.)
I'm looking for a good book on General Relativity, specially on Black Holes and Graviational Waves. I got Schultz book once ago, but it has a fuzzy notation and does not deal with the math as I suppose to. I know the basics of Differential Geometry, Topology...
Homework Statement
Suppose we have a covariant derivative of covariant derivative of a scalar field. My lecturer said that it should be equal to zero. but I seem to not get it
Homework Equations
Suppose we have
$$X^{AB} = \nabla^A \phi \nabla^B \phi - \frac{1}{2} g^{AB} \nabla_C \phi \nabla^C...
I'm trying to understand how the various EM tensors work in General Relativity. The only source I've found is https://en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime, but there are two things I don't get.
Why do they use ordinary partial derivatives instead of covariant ones...
Tidal Forces: "It arises because the gravitational force exerted by one body on another is not constant across it". which implicitly implies that the acceleration is not constant on that body.
Equivalence Principle: "weightlessness sensation occurs when one free falls in gravity" - which...
I'm currently taking a course in Theoretical Mechanics, which is a prerequisite to General Relativity, which I'm very much looking forward to taking. However, I'm not that good in mechanics, and Real Analysis seems to be more straightforward than even the first course in Mechanics. I'm quite...
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...
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...