Gr Definition and 952 Threads

I recently read Einstein's book explaining SR and GR for general readers. Though it was simple, at one place, while explaining proof of GR, he wrote about bending of light near sun to be collective effect of Newtonian gravity and spacetime curvature (half-half). However, GR gravity (spacetime...

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...

These are the EOMs for a 4D space-time that has a plane singularity at x=0. They are simpler than most, but as I've confessed before, I need help with even the simplest DE's. This is not a home-work question. x\frac{d^2\tau}{dt^2} - \frac{d\tau}{dt}\frac{dx}{dt} = 0 x^3\frac{d^2x}{dt^2} +...

obviously the equations of tidal forces and geodesic deviation are very similar to lead one to motivate yourself to explore gravity as not a field but as a curved geometry, Einstein also said that if each accelerated frame is locally an inertial one the euclidean geometry of Lorentz can not...

I was wondering if anyone had an explicit form of the hamilton-jacobi equations for GR. I had a little attempt myself using the 10 components of the metric as the 'co-ordinates', R*sqrt(det(g)) as the Langrangian density, but the maths got a bit messy when trying to compute their canonical...

If this mammoth effort does favour some other model what will the next step be? Will every one try to find fault first?

Do you have a link where I could download video lectures on GR?

I just can't figger it out from their website. Does GP-B have results that are either consistent with or not consistent with the geodetic effect or frame dragging or gravitomagnetism? Or is it that the unexpected errors swamped the difference in gyro alignment that would have been apparent...

According to the official textbook version, the coefficient of proportionality k in the Einstein equation: R_{\mu\nu} - \frac{R}{2} \, g_{\mu \nu} = k \, T_{\mu \nu} is fixed by requiring the equation boils down to Poisson equation for some kind of self gravitating fluid: \nabla^2...

I am sorry for posting this problem again. I posted it in introductory physics and someone mensioned it might not be an introductory physics problem. Any way I still don't have an answer to it so thought of asking you all, thanks. Homework Statement A satellite is in circular orbit of...

I think we have tested experimentally only Minkowski (Special Relativity) and Schwarzschield (Solar system tests) solutions of GR. Am I missing anything?

As an optician, I am uncomfortable with the concept that photons sail through space on geodesics defined by the masses embedded therein. What is the problem with simple refraction, as explained by classical optics? As it turns out, there is absolutely no problem, according to Einstein. In his...

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...

Hello, I am just wondering, when we talk about fundamental forces we refer to the strong force, electromagnetism, the weak force and gravity. But is it not true that gravity is just the curvature of the space time fabric, in which case it is technically not a force. So when we say gravity is a...

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?