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 if this is the right place to post it, but I think the "textbooks" section is'nt. So I'm going to put it here.)
I have been self studying S&G relativity for almost eight months, mostly from Weinberg's book on S&G relativity, but also from papers I occasionally find on web and from...
Hello there,
I have a question (two very similar questions) about the time and phase delay between rotating objects. I want to describe two extreme cases here: I would appreciate any helps.
Case 1
Imagine two observers (people with telescopes maybe) in space that are standing thousands of...
As I understand it, in the context of cosmological perturbation theory, one expands the metric tensor around a background metric (in this case Minkowski spacetime) as $$g_{\mu\nu}=\eta_{\mu\nu}+\kappa h_{\mu\nu}$$ where ##h_{\mu\nu}## is a metric tensor and ##\kappa <<1##.
My question is, how...
Homework Statement
Homework EquationsThe Attempt at a Solution
[/B]
Let ##k^u## denote the KVF.
We have that along a geodesic ##K=k^uV_u## is constant , where ##V^u ## is the tangent vector to some affinely parameterised geodesic.
##k^u=\delta^u_i## , ##V^u=(\dot{t},\vec{\dot{x}})## so...
Homework Statement
To show that ##K=V^uK_u## is conserved along an affinely parameterised geodesic with ##V^u## the tangent vector to some affinely parameterised geodesic and ##K_u## a killing vector field satisfying ##\nabla_a K_b+\nabla_b K_a=0##
Homework Equations
see above
The Attempt at...
Homework Statement
question attached
Homework EquationsThe Attempt at a Solution
Attempt :
Check if ##V^{\alpha}\nabla_{\alpha}V^u=0##
Since Minkowski space, connection tensors/christoffel symbols are zero so this reduces to:
##V^{\alpha}\partial_{\alpha}V^u=0##
where...
Is it really hard to find a solution of a GR equation maybe two planet system ?
Or It could be a different system.I just wonder
1-How much its difficult ( Like can a person calculate those solutions)
2- Whats the boundries (Like we can solve 2 planet system but not 5 etc ? )
3- Can...
Hi,
i got little confused after this conversation
in https://www.physicsforums.com/threads/some-questions-about-light-and-relativity.918094/page-2
There was also this conversation:
So i want to clear the confusion.
As was pointed out to me, in STR mass is defined as m2=E2 - p2, which...
I've been reading Fleisch's "A Student's Guide to Vectors and Tensors" as a self-study, and watched this helpful video also by Fleisch: Suddenly co-vectors and one-forms make more sense than they did when I tried to learn the from Schutz's GR book many years ago.
Especially in the video...
General relativity passes test at Milky Way’s central black hole
by Ken Croswell
For the first time, astronomers use stars orbiting a supermassive black hole to test Einstein's general theory of relativity, finding no sign of a fifth fundamental force.
Links: John Batchelor Show...
Hello,
I have a mess in interpretation of constants in description of movement in GR.
First of all I define Lagrangian ##l=1/2g_{\mu\nu}u^{\mu}u^{\nu}##, and I would like to talk about axial smyetric spacetime (for example Kerr black hole) ##l(r,\theta)##. l is independent from ##t## and...
Currently reading the following document which is a bit of a brain overload at the minute!
Im considering Equation (4.61). It is the general relativistic correction due to the Schwarzschild field for a near Earth satellite when the parameters \beta, \;\gamma \equiv 1. However, as you will...
In coordinates given by x^\mu = (ct,x,y,z) the line element is given
(ds)^2 = g_{00} (cdt)^2 + 2g_{oi}(cdt\;dx^i) + g_{ij}dx^idx^j,
where the g_{\mu\nu} are the components of the metric tensor and latin indices run from 1-3. In the first post-Newtonian approximation the space time metric is...
If we assume I live in Jupiter and there is one year passed in my clock how many years passes in the earth?
And how can I use that Equation in the attached?
In Hawking-Ellis Book(1973) "The large scale structure of space-time" p69-p70, they derive the energy-momentum tensor for perfect fluid by lagrangian formulation. They imply if ##D## is a sufficiently small compact region, one can represent a congruence by a diffeomorphism ##\gamma: [a,b]\times...
Dark matter and dark energy are fudge factors to solve problems in general relativity such as unexplained mass and drag. Is this correct or am I missing something?
I have read Special Relativity from Resnick and Halliday's book Fundamentals of Physics. Now I want to read general relativity.
I tried reading Einstein's book "Principles of Relativity", but sad to say, many things went tangentially above my head because I couldn't follow many equations, as...
I have read that photons do not experience time...
If that's the case then if a particular photon is emitted by a body then that should exist in every time relative to us i.e that same photon should be there at exactly the same point forever.
Hi there guys,
Currently writing and comparing two separate Mathematica scripts which can be found here and also here. The first one I've slightly modified to suit my needs and the second one is meant to reproduce the same results.
Both scripts are attempting to simulate the trajectory of a...
The speed of light (in the vacuum) is a function of the permeability and permittivity of the vacuum. In other mediums the phase velocity will be different. It is assumed (by me) that the speed of a gravitational wave does not change depending on the medium i.e. a gravitational wave would not...
Consider a force-free particle moving on a geodesic with four-velocity v^\nu.
The formula for the four-acceleration in any coordinate system is
\frac{dx^\mu}{d\tau} = - \Gamma^\mu_{\nu\lambda} v^\nu v^\lambda
Since the four-acceleration on the left side is orthogonal to the four-velocity, this...
Last year I've finished the undergraduate course in Mathematical-Physics and Mathematics and this year I've started on graduate school on Physics in order to obtain a master's degree. What I'm really interested are two main topics: general relativity and quantum field theory. I also like...
In his book Gravitation and cosmology, Weinberg derives the perihelion precession of Mercury in the Robertson expansion. The final formula is
\Delta\phi =\frac{6\pi M G}{L} \frac{2+2\gamma-\beta}{3}
The second term is one for GR (β=γ=1).
I have two questions regarding this formula:
1. The...
Homework Statement
Show that the metric connection transforms like a connection
Homework Equations
The metric connection is
Γ^{a}_{bc} = \frac{1}{2} g^{ad} ( ∂_{b} g_{dc} + ∂_{c} g_{db} - ∂_{d} g_{bc} )
And of course, in the context of Einstein's GR, we have a symmetric connection,
Γ^{a}_{bc}...
Homework Statement
Homework Equations
see above
The Attempt at a Solution
Using the conservation equation for ##p=0##
I find: ##\rho =\frac{ \rho_0}{a^3}##; (I am told this is ##\geq0## , is ##a\geq0## so here I can conclude that ##\rho_0 \geq =0 ## or not?)
Plugging this and ##p=0## into...
This past semester, I just took an introductory course on G.R., which translates to a lot of differential geometry and then concluding with Schwarzschild's solution. We really didn't do any cosmology. However, one of the themes that kept creeping up again and again is that in 4-dimensions...
I am doing some mathematical exercises with 3D anti-de sitter face using the metric
ds2=-(1+r2)dt2+(1+r2)-1+r2dφ2
I found the three geodesics from the Christoffel symbols, and they seem to look correct to me.
d2t/dλ2+2(r+1/r)*(dt/dλ)(dr/dλ)=0...
Hi there guys,
I'm struggling! I've been looking at the International Earth Rotation Services (IERS) "standards" for motion of a satellite in GR. the expression is far from trivial and I'm battling to determine where to even start with this bad boy.
The expression is given by
\Delta...
Please, help here people.
Im reading this article Wave Optics in Gravitational Lensing (T. T. Nakamura, 1999) . In the article start work with
\begin{equation}
(\nabla ^2 +\omega)\tilde\phi = 4\omega^2U\tilde\phi
\end{equation}
where $$\tilde\phi = F(\vec r)\tilde\phi_{0}(r)$$. Using...
In the book General Relativity for Mathematicians by Sachs and Wu, an observer is defined as a timelike future pointing worldline and a reference frame is defined as a timelike, future pointing vector field Z. In that sense a reference frame is a collection of observers, since its integral lines...
It is said that GR in the weak field limit it produces Newtons familiar law, so why can't GR produce other formulas for "strong field" which I guess it means at short distances.
I've read Collier's book on General Relativity and consulted parts of Schutz, Hartle and Carroll. In the terms they use, i have yet to gain anything resembling an intuitive understanding of parallel transport.
In fact, it seems to me it is usually presented backwards, saying that the geodesic...
Hello everyone. I was reading Einsteins 1916 original paper on GR, the "The foundation of the general theory of relativity". There are some derivation that he did but I didn't quite understand. It would be nice if someone can give me some direction or some guidance on it.
Here is the link to...
Hello there, suppose we take ##M## to denote the spacetime manifold. Suppose also that ## ds^2 = g_{\mu \nu} dx^\mu dx^\nu##. I have some confusions with regards to the metric and the line elements.
My main confusion is at which points in the manifold are ## ds^2## defined? Is it correct that...
I want to prove that ##E = -g_{\mu \nu}u^\mu p^\nu## is the energy measured by an observer with velocity ##u^\mu## of an object with momentum ##p^\mu##. My reasoning is that in special relativity we know that ##\gamma m = E##. We can transform to coordinates where ##u'^\mu = (1,\vec{0})##. Since...
One way to see that spacetime is curved is to try and draw a "rectangle" in spacetime (see the figure in the Feynman lectures, ch 42.7): If I wait for 100 seconds and then move upwards on earth, I end up at a different point in spacetime than when I first move upwards and then wait for 100...
Hello,
I am new to this forum, but have read a lot of posts and it seems really cool. I am 38 and have a B.S. in mathematics (from many years ago).
I work in insurance, so I am pretty far removed from acedemia now. I have kept up my math studies as a hobby. After studying a lot of theoretical...
Homework Statement
Two plane gravitational waves with TT (transverse-traceless) amplitudes, ##A^{\mu\nu}## and ##B^{\mu\nu}##, are said to have orthogonal polarizations if ##(A^{\mu\nu})^*B_{\mu\nu}=0##, where ##(A^{\mu\nu})^*## is the complex conjugate of ##A^{\mu\nu}##. Show that a 45 degree...
Given the metric of the gravitational field of a central gravitational body:
ds2 = -ev(r)dt2 + eμ(r)dr2 + r2 (dθ2 + sin2θdΦ2)
And the Chritofell connection components:
Find the Riemannian curvature tensor component R0110 (which is non-zero).
I believe the answer uses the Ricci tensor...
Homework Statement
Attached
Homework EquationsThe Attempt at a Solution
So the question says 'some point'. So just a single point of space-time to be isotropic is enough for this identity hold?
I don't quite understand by what is meant by 'these vectors give preferred directions'. Can...
I've thought of a new way (at least I never read it anywhere) of counting the independent components of the Riemann tensor, but I am not sure whether my arguments are valid, so I would like to ask whether my argument is sound or total bonkers.
The Riemann tensor gives the deviation of a vector A...
Homework Statement
I have several problems that ask me to prove that some quantity "transforms like a tensor"
For example:
"Suppose that for each choice of contravariant vector (a vector) A^nu(x), the quantities B_mu(x) are defined at teach point through a linear relationship of the form...
Homework Statement
Question attached
My method was going to be:
set ##r=R## and solve for ##n(R)##
set ##r=2GM## and solve for ##n(2GM)##
I was then going to integrate proper time ##s## over these values of ##r##:
##\int\limits^{n=cos^{-1}(\frac{4GM}{R}-1)}_{n=cos^{-1}(1)=0} s(n) dn ###...
Forgive me if this question is a bit amateurish but i am no physicist. I know in general terms that GR and QM aren't compatible with one another, but my question is...Do they even need to be? can it not be a handoff scenario? why can't GR govern what it is supposed to govern and QM govern what...
Homework Statement
I'm a new one on general relativity
there are two prolems:
first how to certify the proper length of light is zero
second ,how to certify proper length of light ,do not change in all inertial frame
Homework Equations
for second question, probally Lorentz transform,
The...