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.
Hello, Everybody!
I'm new to the board, and am happy to have found you!
I have six questions I can't seem to find the answers to, either in books or online -- yet I know the answers are out there! I'll post each question in a separate thread, and hope that someone who knows far more than I do...
I understand that all physical laws essentially codify mathematically observed behavior. Newton codified Kepler and Brahe data, for example. Quantum Mechanics codifies observed particle behavior at relatively low speeds, etc. But Einstein had no empirical data to work from… So, I do not...
Homework Statement
Suppose everything is moving slowly, How can we find the metric tensor in GR in terms of the mass contained.
Homework Equations
I understand in case of everything moving slowly only below equation is relevant -
R00 - ½g00R = 8πGT00 = 8πGmc2
The Attempt at a Solution
None.
In considering special relativity as a limiting case of the general theory (without matter or curvature) the question arose as to whether the pseudo-riemann nature of the SR metric is actually an independant (essentially experimentally determined) assumption/property or derivable from the...
Homework Statement
Close to a Schwarzschild black hole, a photon is emitted between r = 2(mu) and 3(mu), where \mu = \frac{GM}{c^2} . The photon is emitted at an angle (alpha) to the radial direction. At r = 2(mu), the highest angle that the photon can escape at is (alpha) = 0; at r = 3(mu)...
I am currently learning general relativity and I kind of understand what the symbols in einstein field equationd represent. But I need example like those that involves actual numerical values. I have been trying to search for it online but I cant. So does anyone mind showing me how you apply...
Let's assume the Earth was perfect sphere with radios of 6,750,000 meters.
There are 3 clocks , one will not move one will move west in velocity V and the other will move east in the same velocity.
The Earth is still rotating. So one clock is going with the Earth rotation and the outher is going...
Hello all,
I have a quick question regarding the relation of the space-time metric and the curvature. I have determined the space-time metric, g_(alpha beta), but I am unsure as how to go from the line element ds^2 = [ 1 + (dz/dr)^2] dr^2 + r^2 dtheta^2
and the space-time metric g to the...
Decades have passed since the first idea of General Relativity arose in the mind of Einstien. Surely development of the GR must have taken place during these years. May anyone one update me about these development that took place since the late past.oo):w
Hello,
This spring, I will have the opportunity to do a one-on-one independent study in math or physics. I've narrowed down my choices to differential geometry and general relativity. I'm thinking about the future here- will studying general relativity this spring better prepare me for...
I was recently exploring time dilation from Gravity and from velocity and I came up with an interesting derivation that I have not seen before. I was wondering if there is a paper published showing these relationships like this before and where I could find it?
First you start with the...
Homework Statement
I'm not in grad school but I've been trying to teach myself some GR and I asked a professor what problems he thought would be good to study. He mentioned this one. I'd ask him for help, but he's out of town this week. I've also attached a picture to this problem. (It seems...
So I recently watched the new movie Interstellar, and I've been inspired to do some more general relativity. At one point in the movie they mention that 1 hour on a planet orbiting a black hole is 7 years back on Earth, and so I decided my first project would be to figure out exactly how close...
I can fairly understand the concept of gravity as a curvature in space time in general relativity, but so far I could not understand completely the tidal forces explained by the curvature of spacetime.
When the moon is on one side of the earth, the oceans on this side come closer to the moon...
Consider a flat Robertson-Walker metric.
When we say that there is a singularity at
$$t=0$$
Clearly it is a coordinate dependent statement. So it is a "candidate" singularity.
In principle there is "another coordinate system" in which the corresponding metric has no singularity as we...
Hello!
I hope I am posting this in the right thread!
As I was solving a problem in general relativity, my final answer needs to get a little fancier. So my final answer was as follows: $$ (\bar{U}{U})^3 (\epsilon_{ijk} \frac{d\omega^i}{dx^k} \theta^k) \wedge (\epsilon_{ijk}...
I'm curious about time dilation sizes of below 4 situations. Please assume I'm observing the situations far away in zero gravity. And please ignore all SR effects, just focus on GR.
http://dishdev.me/data/timedilationq.png
Equivalence Principle says acceleration and gravitational fields can...
If you look at Newtonian gravity, there is no major deal with coordinate systems. I am guessing we use coordinate systems because in general relativity we think of coordinate systems as different frames of references and that all frame of references must have the same laws of physics. Is that why?
Is there any book or reference perhaps on string theory or superstring theory or even advanced general relativity that treats the Israel Wilson Perjes metric using the tetrad formalism in details, i.e, 1-forms and so? (Not spinors methos) I have ran across many papers that just place the spin...
We have this stationary metric, $$ds^2 = e^{2U}(dt+\omega_idx^i)^2 -e^{-2U}dx^2$$
The book wrote down the spin connections of this:
$$ \omega^{0i}=\partial_ie^{U}e^0 +e^{3U}\partial_{[_i\omega _k]}e^k $$
and $$ \omega^{ij}= e^{3U}(\partial_{[_i\omega _j]}e^0-\partial_{[_ie^{-2U}\delta_j]k} )$$...
The question that ponders upon the thought if the speed of light really is constant is a fairly common question. However, I was wondering about something and MAYBE this can provide some backup to the theory that the speed of light isn't constant, please point out any mistakes I make in stating...
I am thinking of taking a course on General Theory of Relativity in the next semester of college. My major is in aerospace engineering. I have already completed courses on Calculus, Differential equations, Linear Algebra, and also have a fair bit of idea about tensor calculus.
What other prior...
hello,
I would like to learn general relativity.
To understand general relativity, do I need to understand the math on a rigorous level? (the way mathematicians understand the math) . What math do I need?
Can you suggest me some math/general relativity books?
Thanks and sorry if my english...
Hi.
In class, the professor has tried to derive the equation by using the principle of least-action. (But not yet completed. Maybe next class...)
However I heard this method is used by Hilbert, who had derived the equation 5 days before Einstein derived it.
Then, what method did Einstein use...
Whenever the twin paradox in GR seems to be discussed, it always seems to be done in the presence of a large mass such that the twins can be considered as test particles moving in some metric.
I was wondering whether the same problem could be generalised and be proposed in completely empty...
As some may know, I have been studying the Morris-Thorne wormhole metric for quite some time now.
ds2= -c2dt2 + dl2 + (b2 + l2)(dθ2 + sin2(θ)d∅2)
Now, from this space-time interval, it is easy to see how I would deduce the following metric tensor:
g00= -1
g11 = 1
g22= (b2 + l2)
g33= (b2 +...
I found a new book on The Science of Interstellar by Kip Thorne
https://www.amazon.com/dp/0393351378/?tag=pfamazon01-20
What caught my attention was a photo of John Wheeler at the black board teaching about black holes. You could see the incredible detail in each pane of the board almost like...
I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal representation of the universe:
"Neither does the theory of relativity, Bohr argued, provide us...
Just a quick question. I've recently thought about the various equations I'm learning about calculating velocity or vertical motion and have wondered that sense these equations are using Gravity as a constant force (9.8m/s^2) Is it not true that Einsteins' theory would denounce this idea and...
Homework Statement
An observer is orbiting at a radius r = 3GM, \theta = \frac{\pi}{2} and \phi = \omega t where w is constant.
The observer sends a photon around the circular orbit in the positive \phi direction. What is the proper time \Delta \tau for the photon to complete one orbit...
Hi, I need a beginner's book to study gravitational waves by myself. I am an undergrad physics major and just took my GR course. A beginner's book on GR will also help me lot. please suggest
I am 72 and my background is in the humanities (I read classic authors in Latin and Greek, which I learned in high school in Italy, I love history and I have a more recent M.A. in Philosophy from a Canadian University).
Over the last few years, though, I developed a strong (and totally...
I'm a bit confused about the derivation of the Schwarzschild radius. I can do it quite easily using Newton's Law of gravitation, but this law is only an approximation, so I am wondering whether the result I obtain,
r_{s}=\frac{2GM}{c^{2}}, is an approximation or not. It seems to me that it...
If a rocket takes off from upper part of Earth then it will have to pass the curvature(known as gravity) experiencing gravity which we also experience in reality.But if a rocket takes off from lower part (say antarctica) and moves straight downwards then it would not have to pass the curvature...
If I want to take the wedge product of $$\alpha = a_i\theta^i $$ and $$\beta = b_j\theta^j$$ I get after applying antisymmetrization,$$ \alpha \Lambda \beta = \frac{1}{2}(a_ib_j - a_jb_i)\theta^i\theta^j$$
My question is it seems to me that antisymmetrization technique doesn't apply to the...
Hello Everyone,
I have read many derivations of Einstein field equations (done one myself), but none of them explain why the constant term should have a $$c^4$$ in the denominator. the 8πG term can be obtained from Poisson's equation, but how does c^4 pop up? Most of the books just derive it...
Hello! I'd appreciate any help or pokes in the right direction.
Homework Statement
Show that a co-tensor of rank 2, ##T_{\mu\nu}##, is obtained from the tensor of rank 2 ##T^{\mu\nu}## by using a metric to lower the indices:
$$T_{\mu\nu} = g_{\mu\alpha}g_{\nu\beta}T^{\alpha\beta}$$
Homework...
I've been learning the Israel formalism (see original article here) for thin shells. I think I understand the formalism well and how to do the matching given two manifolds (that are solutions of the Einstein's field equations - EFE).
I've been studying several articles that use the matching...
Dear all,
In one of his lectures,Prof. Susskind mentioned that the event horizon "bulges" forward to meet any incoming radiation or matter; and it is a property of Einstein field equations. I have not come across any such property, and if it exists, shouldn't it belong to the Schwarzschild(or...
This seems like a question that would be in the Relativity FAQ, but I didn't see it.
Briefly: I've seen the claim made that there is plenty of observational evidence for the existence of black holes. But I don't understand how, from the outside, one can tell the difference between a black hole...
A map h: = T.(M) ---> T.(M) is defined by h(X) = X + g(U,X)U where U ε T.(M) is a fixed vector with g(U,U) = -1.
i: Give an expression for the components h^i (sub) j (This is "h" with a superscript i and subscript j) of h regarded as a tensor type (1,1)
ii: Prove that h^2 = h. Interpret h...
I have always been confused about time dilation in General Relativity.
In the twins paradox, it is the traveling twin that ages slower. However, could you not just as easily say that it is the non-traveling twin that is moving away from the other?
So why is it the traveling twin and not...
Alright, I'm rather new to General Relativity, and I'm getting confused with four momentum. Back in SR, p^α=mU^α, but, this relationship doesn't hold in curved space, does it? Because, now I'm seeing that four momentum is somehow a covector in GR, and p_0=-E, so the time component of the...
For example at very low speed (v<<c), in Special Relativity, we can approximate relativistic motion to Classical Newtonian motion.
But in General Relativity, what situation can make there an approximation to Newtonian Gravity
( just like v<<c ) ?
Thanks.
hi fellas,
I want my undergrad thesis on general relativity. I need a good book on einstein field equations and its exact solutions to work with. also a book where are some solved problems and some exercises to guide me to right track
any suggestions ?
regards
Hi,
I started reading General Relativity but concepts such as Lorentz transformations, rotations, tensors etc. are, at least in my opinion, poorly explained. Or perhaps the authors assume that the readers are already familiar with such maths?
At any rate, I would very much like to read...
Has this idea been recognized outside Frankfurt?
http://arxiv.org/abs/0812.1738
Pseudo-complex General Relativity
Peter O. Hess, Walter Greiner
(Submitted on 9 Dec 2008)
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new...