Gr Definition and 937 Threads

I'm looking for absolute basic but respectable introductions to QFT and GR. Any choices? What level of QM is recquired to learn QFT?

Hi all! I'm a first year physics student and I've got some questions I'm hoping someone is able to enlighten me on. Since I'm only in my first year and I haven't had a full course on GR, I'm most likely to have made some errors, so please point out the flaws in my reasoning and gaps in...

My understanding is that in GR the way in which the components of the metric tensor can vary from location to location in spacetime is determined or constrained by a number of factors: (1) the choice of coordinates (a mathematical constraint); (2) the distribution of mass/energy (a physical...

Hello, does anybody know a proof of the equivalence (or differences) between the "total mass" integral \int T_munu \xi^mu dV^nu and the "Komar mass" integral \int R_munu \xi^mu dV^nu ? (here \xi is the timelike killing vector, dV is a 3-volume, and spacetime is assumed asymptotically...

Lisa Randall said "string theory reproduces GR in 10 dimensions" Does string theory gravitons have 4D GR as its low energy limit? I know that its lowest mode vibrations corresponds to a massless spin-2 particle, the graviton. I know GR in 4D can be extended with susy. Does it reproduce...

Hello everyone! I'm on my 2nd graduate year and (unfortunately) just started learning GR. My professor suggests Dirac's textbook for a 1st contact and Wald for further details and advanced topics. I find Dirac too laconic and Wald pretty difficult. So...any other suggestions out there? I've...

Does anyone have a good idea of how big the holes are in our current knowledge of the differential geometry and topology that would make general relativity a much better understood area of research? Or are we already fully equipped in that regard and only need to seek further physical...

I would appreciate if some learned folk could answer these questions to increase my understanding. 1. Does GR support standing wave solutions to the equations? 2. Do physicists study these standing wave solutions? 3. Is it correct to describe GR equations as wave equations? (e.g. as...

GR as a Gauge theory ?? don't know if this is true or not, but i have been reading books by ROvelli (LQG) or 'Gauge theories' the question is could we study Gravity as the set of functions A_{\mu}^{I}(x) Then we write the Einstein Lagrangian (or similar) as: \mathcal L =...

I heard a general theory of relativity was constructed based on MOND rather than on Newton's law of gravitation. How well do the predictions of the MOND GR compare with the classical tests of GR (such as light bending)? Basically, is it in better or worse agreement with experiment than...

How can "empty space" expand? (Reality behind the GR equations.) I have a question - with some concerns over how it may be answered. On other websites, and in other print publications, I've seen Ph.D. physicists and cosmologists misunderstand the question: What does it mean when we say that...

How do we formulate the two body problem in Gr. Also if possible how do we solve it, or approximate said solution?

1. How would a general relativist explain why an object falls towards the earth? 2. Is it correct to say that it is not the apple that falls towards the Earth but it is the Earth that accelerates towards the apple? Why is this ok to say? Is it because, in GR, there are no preferred reference...

Hello all, I, by no means, fully understand general relativity. I was wondering if one of you experts could help me clarify some things, as I am giving a presentation to my class on GR next monday. We are in a somewhat basic physics class, so I really just need to get the idea across. From my...

From http://www.us.oup.com/us/catalog/general/subject/Physics/Relativity/?view=usa&ci=9780198567325" I learn that the fundamental identity c^2\text{d}{t'}^2 -\text{d}{x'}^2 -\text{d}{y'}^2 -\text{d}{z'}^2 = c^2\text{d}{t}^2 -\text{d}{x}^2 -\text{d}{y}^2 -\text{d}{z}^2 relates co-ordinates...

I have been told that using a metric g_{00} = -a^2(\eta)(1+2\psi) g_{oi} = g_{i0} = a^2(\eta)\omega_i g_{ij} = a^2(\eta) \left[(1+2\phi)\gamma_{ij} + 2\chi_{ij} \right] and a gauge transformation x^{\bar{\mu}} = x^{\mu} + \xi^{\mu} with \xi^0 = \alpha \xi^i = \beta^j gives...

i am a physics enthusiast studying general relativity on my own with the book: "Exploring Black Holes: Introduction to General Relativity" by Edwin F. Taylor and John Archibald Wheeler. I am having the hardest time with the fourth chapter of the book and especially the 4th question in that...

As I mentioned a while back I was starting a new project so I wouldn't be posting much until I was finished. The project was for me to take all my files (all physics articles) from the two draws in my cabinet and scan them and place them in PDF files. That work is now complete. The list of...

I read a statement on another message board the SR forbides BHs and GR demands them. Does SR forbide Black Holes, if so, why?

I am trying to understand how they find an exact solution of Einstein equation and the field equations for the matter fields. My problem is that in GR the coordinate system cannot be chosen independently from matter from the very beginning like in Newtonian mechanics. For example, in...

My understanding of GR is very coordinate oriented which kind of drags me down when I try to answer more general questions. Can somebody recommend a book in Differential Geometry with application to GR? Here are my preferences. I don't like hand waving typical for some books 'written for...

Homework Statement In my GR final, there was a question that asked to show that the horizon r=2GM is a null surface, i.e. d\tau^2=0. How does that work, since just plugging r=2GM and dr=0 in the Schwarzschild metric yields d\tau^2=-(2GM)^2d\Omega^2 which is obviously not zero. :confused:

Original motivations for GR?? I'm sitting here and wondering what was Einstein trying to do when he "discovered" GR? For instance, the biggest motivation for SR was the apparent constancy of the speed of light. That's the problem he was trying to fix. What was it for GR? Was it just the tiny...

I am looking over the Project A: Global Positioning System is Exploring Black Holes; introduction to General Relativity by Taylor and Wheeler. At first, they convincingly suggest that the time dilation caused by the differences in radius from Earth clocks to the satelight clocks will cause the...

It is possible to draw world-lines of the two twins in the non-accelerating one (A) frame of ref. The aging of the other (B), with respect to the first, is evaluated integrating its proper time differential (and comparing it with A's proper time). My question is (certainly already asked): is...

Homework Statement We have a vector X^a (n.b ^ indicates superscript) and covector Aa. We need to show that X^b (d(Aa)/d(x^b) - d(Ab)/d(x^a)) transforms correctly under an artbitrary smooth change of coords. N.b the derivatives are partial. By using the transformation rules for the...

Hi folks, I'm looking for some interesting questions/challenges regarding linear algebra and general relativity for fun. I'm particularly interested in tensors, but my background here is a bit weaker. Just wondering if anyone has any thoughts or ideas? :cool:

Ok thhe follwoing questio is extremely silly. everything else that I've read in the book makes sense but this part doesn't. i just can't seem to udnerstand it because of a combination of stupidity and notation. Near the end of page 69 an identity is derived to show how the components of the...

Homework Statement Find the orbit of a planet in a grav. field corresponding to the metric d\tau^2=(1+\alpha^2(x^2+y^2))dt^2-(dx^2+dy^2+dz^2) in the Newtonian limit with the initial conditions at t=0, x=R, dx/dt=\beta,0=y=z=dy/dt=dz/dt where alpha and beta are cositive constants. Homework...

Homework Statement An observer atop a tower of 10m on Earth sends a signal towards the base of the tower every second according to his clock. The gravitational field corresponds to the metric. d\tau^2=(1+zg)dt^2+\frac{1}{1+zg}(dx^2+dy^2+dz^2) (where g~10m/s²) An observer on the...

Homework Statement An observer in a rocket is in a circular equatorial orbit arounda planet and the period of the orbit is the same as the period of revolution of the planet. The planet has mass M = 1033kg and radius R = 1000km. The observer sends a signal every 20 seconds according to its...

We consider a 2 dimensional spacetime with coordinates (t,y) and metric g=dt\otimes dt - (t^2+a^2)^2dy\otimes dy where a is a positive constant. In previous subquestions, I have calculated the Christoffel symbols for the metric-compatible connexion and now I am asked to find the null geodesic...

Hello, I have a friend who likes physics as a hobby (like me) and will have his anniversary soon. He owns already a nice collection of classics, including MTW for example. His oldest son just started physics at university. What would you suggest as possible gifts for this friend? I...

Homework Statement Consider a 2-sphere of radius R parametrized by the 2 spherical polar coordinates θ and φ. Write down the standard metric in these coordinates. 1. Show that lines of constant longitude are geodesics, and that the only line of constant latitude is the equator. 2. How...

Is there a method to describe GR without using coordinates or metrics g_{ab} , x_{a}(s) , using only Analytic or Algebraic methods?, the main problem with a geommetryc aspect is that you can't use it when dealing QM since at this level there is no Geommetry.

If we have Einstein-Hilbert Lagrangian so: \mathcal L = (-g)^{1/2}R for R Ricci scalar (¿?) then my question perhaps mentioned before is if we can split the metric into: g_{ab}= Ndt^{2}+g_{ij} dx^{i} dx^{j} N=N(t) 'lapse function' then i would like to know if somehow you can split...

For a 2 body problem in GR, will the metric be that due to one body, or both bodies?

"Hidden variable" in SR and GR Relativity??.. My question is, since we live in a 3-D world, what would happen for an "alien" living on a 4-D world??..if we suppose that space-time has only 4 dimension, and that after a Wick rotation then X_{0} =it then what we think is just a time component...

Homework Statement The acidic waste from a student's experiment needs to be disposed of, but pouring it down the sink would increase the impact of acid rain on the local water supply. Explain how you could determine the amount of limestone needed to neutralize the environmental impact of the...

Sorry if you have already covered this subject. Is it possible to apply the formula F = -GMm/R^2 for a relativistic particle substituting m with its relativistic mass?

the "future" in GR In GR, is all of time already contained in ST and we're just moving through it? this seems to be the only way to explain the fact that for different observers time passes at different speeds. is this correct? (this isn't a philisofic question)

From my very limited knowledge of General Relativity, i have the impression that mass is just considered as 'other' in this theory. By that i mean, GR assumes matter to be made of something other than space-time, and only deals with the effect that matter has on the geometry of space-time. Is...

I'm just curious as to how GR doesn't allow this. --thanks.

When I first read about accelerated expansion in 1999 I immediatelly thought of gravitational repulsion between matter and antimatter. I know it is an old idea, and very much out of the mainstream, but when you read reviews about the arguments against it, it really makes you think. It is a case...

Aboslute time in GR?? :shy: although for Einstein fans this post could be a "blasphemy" .. my question is if under some assumptions we could derive (or at least an approximation to ) GR in a way so there is some kind of "absolute time-frame" of reference for every observer in the universe of...

What are the incompatibilities between GR and QM?? appart from the fact that GR is NOn-renormalizable (perturbatively :rolleyes: ) since there are almos infinite types of UV divergences \int_{0}^{\infty}dxx^{n} n=-1,0,1,2,3,4,... What other incompatibilities are there?..if space weren't...

The Rindler geometry and its horizon can be obtained by a simple succession of Poincaré transformations to match the frame of an accelerated observer. By combining this SR result and the equivalence principle it follows that a uniform gravitational field is represented by the Rindler metric and...

I understand why it is so desirable to be able to write all the laws of physics by the same rule in any system of coordinates. I also nearly understand that the equivalence principle leads to the need of curved spacetime. But how to make that as obvious as possible? Thanks, Michel

If we apply the Bohr-Sommerfeld quantization to GR (semiclassical) \oint_{S} \pi _{ab} dg_{ab}=\hbar (n+1/2) :confused: :confused: In this case if "Energies" (or whatever you call energy since in Quantum GR H=0 for the "Hamiltonian constraint" ) then using Einstein equation we see that...

I think that in Special Relativity, the drift of the perihelion can be calculated by cumulating elementary Lorentz transformations along the (Newtonian, unperturbed) trajectory. I read that the result of this calculation is much smaller than the experimental value. It is also well known that...