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.
Is gravity strong enough to attract 2 galaxies togeather in Gr..I mean is gravity present everywhere in the universe or are there places in universe filled with vacuum and has no gravity waves through it.?
Use the metic that Einstein proposed in the first cosmological model based on general relativity.
ds2 = -dt2 + (dr2) / (1 - Kr2) + r2(dθ2 + sin2θd\phi2) where K > 0
Show that the stress energy tensor is that of a static, spatially uniform perfect fluid and determine ρ and p in terms of G and...
Can one detect length contraction due to general relativity? I.e does length/width/height change with distance to a gravitational centre? If so does the object get longer or shorter?
I know this is the case with increasing speed in special relativity, but what about GR...
If i went into...
I'm not sure if this is the right place to post this topic, but I need some opinions.
I would really love to learn General Relativity. I possesses a working knowledge of tensors (namely tensor calculus and analysis).
Upon doing some research I was told Gravitation by Misner, Thorne, and...
Suppose we have two bodies of equal mass m and with hyperbolic motion and with small, fixed impact parameter.
Now let's assume the speed of the two bodies in the c.o.m frame approaches c.
Is there a way - with a delta-function ansatz for the energy-momentum 4-tensor - to understand the...
Homework Statement
Show that Gij = Gji using the Riemann tensor identity (below)
Homework Equations
Gij = Rij - 1/2(gijR)
Rabcd + Rbcad + Rcabd = 0
R = gmrRmr
Rmr = Rmnrn
The Attempt at a Solution
I have tried to put the Ricci tensor and Ricci scalar (from the Gij...
In relativity, proper time along a world-line is be defined by d\tau^{2} = ds^{2} / c^{2}
However, proper time can also be understood as the time lapsed by an observer who carries a clock along the world-line.
In special relativity, this can easily be proven:
The line element in special...
It had been my understanding that the big bang model of the universe is a theory of the origins of the structure of the universe in which the expansion of the universe is extrapolated back in time until we arrive at a near-singularity and general relativity breaks down. Accordingly, the big...
From the special relativity theory , for explaining the red-shifting of a photon, that has been red-shifted, is the following:
point O: origin point of emitted photo, in Galaxy GlxO
point R: receiving point of photon, in Galaxy GlxR
GlxO, O ---------->----------------R, GlxR
Suppose...
Hi there,
I am wondering if anyone might be ablet to suggest a good book to give me a working knowledge of general relativity. I have already sat a "relativity and cosmology" undergraduate module but I find that I am still unable to understand papers on gravity. I would like something that is...
Consider the following, from the prospective of General Relativity:
A photon's path between two points, point O (emitted point, from galaxy GO) to point R (received point, in Galaxy GR):
O: point of photon's origin, in space
GFO: gravitational field force at point O, due to its position in...
Hi!
I'm reading General Relativity by Wald. In chpater 4.4a about Newtonian limit of linearized gravity, it says:
"When gravity is weak, the linear approximation to GR should be valid. The assumptions about the sources (relative motion << c and material stresses << mass-energy density) then...
I see where someone listed a theory that they had https://www.physicsforums.com/showthread.php?t=49230
so going to attempt to do the same.
I listed my theory at http://www.bautforum.com/showthread.php/129309-Negative-Mass-Interpretation-of-General-Relativity but they are very quiet and I would...
I am a first year undergraduate who in my spare time is desperately trying to understand what happens when General Relativity and Quantum Mechanics are 'merged'.
Almost all of the searches I have done on the subject have turned up with
the same similar statements:
'General Relativity and...
I am looking for papers, books or any other resources which I can use to work in General Relativity with Maple.
I know, there is GRTensor tool, but it is not up-to-date as far as I understand from its website (latest test was on Maple 11). I use Maple 15.
Can you advise me something?
I have very little knowledge in general relativity, though I do have a decent understanding of
the theory of special relativity.
In special relativity, points in space-time can be represented in Minkowski space (or a hyperbolic space) so that the metric tensor (that is derived in order to...
Homework Statement
What is the speed of a particle in the smallest possible circular orbit in the Schwarzschild
geometry as measured by a stationary observer at that orbit? Note: The orbit in
question happens to be unstable.
Homework Equations
Normalization condition...
Homework Statement
I have a problem. I need to prove that the divergence of Einstein tensor is 0 using the bianchi identities. I have looked to several sources and I have derived an answer, but I don't fully understand some steps.
Homework Equations
I have uploaded a document which shows a...
Homework Statement
I'm staring down a concept homework assignment that is giving me fits. We are just moving into relativity.
6) The quantity γmc^2 represents...
a) the rest mass energy.
b) relativistic kinetic energy.
c) total relativistic energy.
d) relativistic momentum.
e) None...
for general relativity, all i see on the internet is a bunch of statements clustered together: "oh yeah, general relativity is pretty important and explains black holes, time dilation, and gravitational lensing"
but what is it? at a point that has more energy, time goes faster? in other words I...
Homework Statement
A spaceship is moving without power in a circular orbit about an object with mass M. The radius of the orbit is R = 7GM/c^2
(1) Find the relation between the rate of change of angular position of the spaceship and the proper time and radius of the orbit.
Homework...
Homework Statement
I attach a word document with the equations because I don't know how to write them on the post.
My question reads: Show that Maxwell's equations Eq (1) is equivalent to Eq (3).Homework Equations
The first term of Eq 1 reads: F sub alpha beta comma gamma. That means partial of...
hi
I understand that Snell's law describe the relationship between the angles of incidence and refraction, when referring to light passing different isotropic media.
someone told me that Snell's law describe also the curvature of space time in General Relativity? is that true? if not what are...
Homework Statement
A thought experiment. Imagine ants living on a merry-goround,
which is their two-dimensional world. From measurements
on small circles they are thoroughly familiar
with the number pi. When they measure the circumference
of their world, and divide it by the diameter, they...
Exercises of Schutz's "First Course of General Relativity"
Dear all,
does anybody know where solutions to the exercises can be found?
I remember that I found a link in the Web once but I forgot where.
Thanks,
Goldbeetle
My understanding of the proof goes like this
x -star
| --- light ray
|
| O -sun
|
o -earth
The light ray is seen to bend a tiny bit when it reaches earth.
My question is this. If we forgot about relativity and assumed the light had a tiny but finite mass (like 10^-100 kg)...
After recently researching about Quantum Field Theory and more specifically gravitons, I am slightly confused with how this theory of the gravitational force fits in with general relativity. I know it hasn't disproved it so there must be some connection. Do gravitons in 11 dimensions cause...
What are the equations from which all of GR can be derived? Obviously one of the equations is Einstein's Field Equation: G^{\alpha\beta}=8\pi T^{\alpha\beta}. I would also guess that you would need the Euler-Lagrange Equations: -\frac{d}{d\sigma}(\frac{\partial L}{\partial...
Hey there,
In my university, General Relativity is listed among elective courses (along with an advanced quantum mechanics course). I'm curious to know whether general relativity is really an undergrad course or not. And what are the pros and cons if GR is taken in grad school?
Thanks for...
So the principle of equivalence states that any effects due to acceleration must also occur with gravity, as it's impossible to tell the two apart. I get that, but it assumes that gravity exists and you know how much it accelerates objects.
But that explanation just predicts what will happen...
I'm a bit confused by the following:
We can derive the equation of motion for a particle traveling on a timelike worldline by applying the Euler-Lagrange equations to the Lagrangian
\mathcal{L}=- g_{\mu \nu}(x(\tau)) \frac{d x^\mu}{d \tau} \frac{d x^\nu}{d \tau}
However, to derive the...
Hi,
I'm trying to understand a derivation / question for my revision. It has to do with the four momentum of a photon and doppler/redshifts.
Homework Statement
Show that ratio between emitted and received frequencies (for two observers E and R moving with velocities u and v respectively)...
I'm going through Landau/Lifgarbagez's book II of theoretical physics. In it they have a derivation of the equation of motion from the principle of least action, however I don't understand one step.
Homework Statement
Derive the equation of motion:
\frac{d^2x^i}{ds^2}+\Gamma^i_{kj}...
Hi! Need some help here.
Are the effects of general relativity reciprocal in two reference frames? Let's say for example that there is one man at the bottom of a really, really tall building, and another at the top. The man at the top floor should perceive the man at the bottom to be...
Hi Everyone.
I have just created an animated video on Special and General Relativity, explaining how all the conclusions are derived from the fact that light has the same speed for all observers.
It is at:
http://youtu.be/ev9zrt__lec
I put a lot of effort into making the animations, so...
Generally speaking, what physics and math should one be comfortable with before taking a course on General Relativity? If it helps, the course will be using Shultz's A First Course in General Relativity.
I am about to start my thesis and I have, let's say, just an introductory course of General Relativity as background and I would like to know which would be a good book as a reference so that I can get a stronger knowledge of General Relativity.
All this taking into account that I will do my...
Homework Statement
A satellite is in circular polar orbit radius r around Earth (radius R, mass M). Clocks C on satellite and C0 on south pole of earth. Show the ratio of the rate of C to C0 is approximately
1 +\dfrac{GM}{Rc^2} - \dfrac{3GM}{2rc^2}
Homework Equations
d\tau =...
I saw that if you combine the quantum mechanics theory whit the general relativity you remain whitout time. So the time can be an ilusion, but i don't believe that . What you think about it ?
I remember reading a long time ago that there was a straightforward (but operationally difficult) way of constructing General Relativity from the Linear Field Equations. Essentially you start with the Linear Field Equations solution and then generate a stress energy pseudo-tensor for this...
Hi everyone!
I'm really sorry to bother you with my surely stupid questions, but I am 13 years old and today I read some lines about Special Relativity and General Relativity at school and found myself stuck on some thoughts I can't cease to think about... I really hope that you will be so kind...
Everyone is congratulating the recent Nobel Prize winners, whose work uses observations of distant supernovae to attempt to show the existence of universal acceleration.
Let's not forget that supernova studies of cosmology are all based on a theory (General Relativity) that has huge problems...
Does Quantum Field Theory and General Relativity Theory predict anything which is mutually exclusive? This question came up to me as i was thinking about why there was/is apparent rivalry/debate between the proponents of these two theories.
As far as i understood, Universe(or Multiverse) is...
Hello,
I am wondering,
if I am sitting on my chair, here at home, planet Earth, am I accelerating (in GR)?
Does the tangent four-vector u to my worldline obey the equation
\nabla_{u} u = a
or instead
\nabla_{u} u = 0
??
and if the first one is correct, is the four-vector a constant?
I've completed college-level special relativity, which includes length contraction, time dilation, the Lorentz transformations, momentum and energy. What additional mathematical and physical knowledge do I need for starting to read general relativity?