Gr Definition and 937 Threads

Are there any good references out there for writing the equations of GR in matrix format? For example: ds^2 = g_mn dx_m dx_n -> ds^2 = dx+ g dx where the matrix version of g_mn (g) would be hermitian, dx+ is the conjugate... covariant derivative: Y_n||m = dY_n/dx_m - {n, km}...

1. A (presumably) simple question: We are used to think that the affine connections emerge whenever one wants to differentiate a vector (tensor, spinor) on a curved manifold in general relativity. Now suppose that we are still on a flat background of special relativity, though in a...

Hello all, this is my first post on this forum, though I have been perusing it for a while. I am currently re-reading through Carroll's text on SR and there is a curious comment on p24 that intrigues me. Carroll says that the *only* tensors in SR which are invariant are the Kronecker delta...

I apologize for the poorly worded title. Let me try to explain my question better. A scientific theory must be predictive to be useful. Since we only know what happened in the past, the global topology of spacetime cannot be an input to the theory. Given space-like slices/"chunk" of the...

Sean Carroll has an excellent account of a new paper by Rachel Bean. I don't always share Carroll's attitudes or appreciate his reporting, but here's a case where I thought his post was top notch. You may have already read his posting and if not I hope you will. Meanwhile let's take a cue from...

I read that General Relativity reduces to Newtonian when v<<c as well as when Newtonian gravitational potential energies are small compared to mc^2. What is the GR version of gravitational potential energy?

Hi, What are the weaknesses of Einstein's GR ? Why people are trying to construct GR from field theoretical point of view... all because of quantisation?

I am currently taking a GR course and I am finding the following quite useful: Ruslan Sharipov's Website has some GR relevant material, specifically books number 3,4, and 6. These books are free, as you will see is stated within the first few pages of the book. Also...

A little question which I thought of today. I thought about what happened in a medium with Lorentz transformation. With a refraction index n, the speed of light is altered to c/n. However, as far as I can see now this shouldn't influence the Lorentztransformations, right? It's tempting to put...

Hi again, Thaks for previous help. I am self studying GR using Schutz and Dunsby's webpages & notes. I am stuck on a step in the derivation of the weak field approximation. They approximate the metric with g[a][/b]=n[a][b]+epsilon h[a][b] In step 7.30 the partial derivative h[i][0],[0]is...

I am interested in the correspondence between reality and the mathematics of spacetime and wonder if that is an issue with anyone else? How is the question of correspondence handled in teaching students about General Relativity? I characterized the issue of correspondence as follows and...

Homework Statement This is a problem in General Relativity, where I am trying to find the Christoffel symbols that correspond to a given metric. Any help would be greatly appreciated! OK. I have been given the metric ds^2 = (1+gx)^2 dt^2 - dx^2 - dy^2 - dz^2 and have been...

as a field acting over a spacetime metric (rather than encoding it in the metric) but still reproduce key GR results including time-varying phenomena?

Hi everyone. Schutz recently released a 2nd edition of his book "A First Course In General Relativity". Has anyone read this edition? Is it worth getting the 2nd edition, or is the 1st fine? The library has the first edition and that's 390 pages. The second edition is 410 pages. From the...

Gravity seems to squish space time, velocity seems to also. It seems that through each's affect on distance, a formula containing both could possibly exist. Also, if we stopped and considered GR a law instead of a theory for a moment, then we conclude singularities must not exist. And QM...

I've never taken a class on GR, but I've been looking at books on the subject. Clearly, Einstein's equations for GR must reduce to Newton's law of gravity, but how? I haven't seen it worked out anywhere. Can someone send me a link, or show a proof or derivation? Like I said, it's not...

One of string theory's triumphs is the post-diction of a spin-2 field, which is supposed to represent gravity (GR). Yet, only in the weak field limit ("linearized") can it be shown that GR is a spin-2 field. So here's my question: why are string theorists confident that they have post-dicted...

I've been given Gravitational Waves: Theory and Experiments Volume I to read for a project. The problem is, I haven't learned General Relativity to a high enough level and the book is proving very difficult for me. The book dives straight into linearised gravity in the first chapter, and the...

Consider a 4-coordinate system x=(x^0,x^1,x^2,x^3), x^0 plays a role of time, x^1, x^2, x^3 are some kind of space coordinates. In what follows greek letters will be 1,2 or 3, latin will be 0,1,2,3, c = 1, proper time squared ds^2 = g_{ik}(x) dx^{i} dx^{k}. Now, if the body is "at rest" we...

Unification of Gravity versus General Relativity -- The Ubiquity of Contradiction Is it just me or is something smelling rotten about unifying gravity with the fundamental forces? Didn't science unanimously agree that Einstein's "Theory of Relativity" correctly explained gravity as not a force...

I'm by no means even adequate in the field of General relativity, so if my question is dumb, please excuse me. Anyways, so I know that from the EFE's you can get the metric for the space-time you are considering, and from this metric you can get the geodesics of this space-time using...

Hey folks, I've been looking for a good biography of Einstein, but I'm especially interested in the story of his development of relativity (both of them!) from a technical standpoint. Most of the Einstein bios at, say, the local Barnes and Noble are geared towards a general audience and have...

Interest is gathering around unimodular General Relativity, so we should get some reference links together to facilitate following the research excursion into that area. Einstein came up with unimodular GR around 1919, shortly after he proposed ordinary GR. Here are some recent (and...

I know that GR is essentially a Riemann theory w/o Torsion; the Levi-Cevita-Connection is symmetric and therefore the torsion vanishes. What happens when fermions are included? Does the spin-connection still guarantue that the covariant derivative comes with a torsion-free connection...

Dear all, what are the differences between Caroll´s GR published book and the PDF text? Thanks, Goldbeetle

I've had a debate with someone recently about whether or not light is constant in GR. I think that it is. Is there any debate on this point?

I tried to search everywhere but couldn't find an answer, so here it goes. In Newtonian mechanics, the gravitational acceleration g at a distance r from the gravitating object is given by Does this equation apply in general relativity aswel? If not, what is the equivalent in GR, ie...

I have a question on finding a specific solution to Einstein's Field Equations. This is purely for my own curiosity. Suppose you were given this picture. How would you find the curvature of the point directly beneath the Earth in the picture, i.e. the point in which the space-time is...

This isn't homework but since it's a simple algebra thought I suppose it's the most appropriate forum- I'm working through some basic general relativity and just came across a line i think I'm being stupid about: g_{\bar{i}\bar{j}}=\Lambda_{\bar{i}}_{i}\Lambda_{\bar{j}}_{j} g_{ij} then, it's...

could GR generalized to non-integer dimension?? let us suppose that the dimension of space time is NOT an integer then , could we generalize GR to obtain an expressions of Tensor, Covariant derivatives... in arbitrary dimensions ?? let us say 4.567898.. or similar, i mean GR in non integer...

The gravitational force is zero at the center of a planet, but the GPE is at a peak minimum (most negative). What happens to the time dilation factor inside the surface of a planet of uniform density versus at the surface of that planet.?

So I'm reading these notes about differential geometry as it relates to general relativity. It defines a tensor as being, among other things, a linear scalar function, and soon after it gives the following equation as an example of this property of linearity: T(aP + bQ, cR + dS) = acT(P, R) +...

Just seeking a bit of guidance if I may ? If Lambda 1 is the time dilation caused by a gravitational field (ie proper time outside field/proper time inside field for static observers), and Lambda 2 is the usual time dilation under special relativity for a moving body (both lambda's >= 1), how...

Homework Statement From Gravitation by Misner, et al. Can anybody who has access to this text show me how to vary this functional from exercise 7.1, and using the principle of least value, derive an identity? The functional is I = [tex]\int[/L d[4][/SUP]]x, where L =...

Dear relativists, I have problems trying to understand the following statement in Forces from Connes' geometry I would appreciate if somebody with a better understanding of GR could elaborate. I know there is no proper general local definition of gravitational energy but I always had...

I will quote him, with his permission: ", I gave a talk a few months ago at P.I. on my research on finite states in QGRA. It was realized during the talk that I would have had to have solved the initial value problem of GR, in order to quantize it by my method. They didn't believe it at...

I wanted to check with you a list of open, unresolved questions in GR. It is well known that GR is not compatible with QM, so obviously there are many unsolved mysteries on the QM level. However, here I wanted to focus exclusively on a small subset of questions: not related to QM, LQG...

A football kicker on his own 34 yard line wants to kick the ball so that it lads on the 1 yard line of the opposing team - for those of you who don't know about football, this is a 65 yard kick - use yards for this calculation not metres. The kicker can kick the ball at 27 yards/sec/ The kicker...

As someone who has never gone through a formal study of GR and SR and whose knowledge of these subjects is at the most basic level I am glad to have found this site because by reading through the threads I am able to pick up interesting snippets of information.What I would like to ask is are...

1.a) Concider the 2-space consisting of a spherical shell at constan radius, r. In polar coordinates the line element on the surface can be written (a, b,∈ 1,2) Homework Equations ds2=gabdxadxb=r2dθ2+sin2θdφ2 calculate gab, Γabc, R1212, R2121, R11, R22, R The Attempt at a Solution...

I cannot get past thinking of it like air pressure

While studying the Einstein Equation, I noticed something curious, at least to me with little experience in General Relativity. Start with the usual formulation of the equation: R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R + g_{\mu\nu}\Lambda = \frac{8{\pi}G}{c^2}T_{\mu\nu} Then, apply the...

Hi. I have a question to ask the countless physics students on this forum. I just completed my gr 12 physics course (SPH 4U) and I absolutely loved it! The teacher was awesome, he had so much passion for the subject and he would go out of his way to tell us about how he majored in physics...

My question is to what extent the specifically non-linear properties of GR have been analyzed by theoretical physicists. Can they give rise to chaos and complexity, as many non-linear systems do? I also wonder: I've so far mostly read about linearized descriptions of gravitational waves...

I mean, why there are so many speculations? It must be 'shut up and press enter' :) For example, some people say that the second horizon in the Kerr black hole is not dangerous. Others claim that due to infinite concentration of energy there there is a real singularity there so everything...

How did Einstein come to pushish his general theory of relativity? Was it in a series of papers over a few years, or in one definite article? In either case, are these (or this) papers available on the internet in engligh? Thanks.

Hi all, I'm taking an introduction to general relativity course along with an elementary differential geometry course this term. I'm really interested in this stuff and I've been waiting 3.5 years to take these courses, so I'm really excited. Which textbooks have you all come across that...

As suggested by Marcus, I have read the whole paper and decided to start a discussion of Kober's paper by asking a few questions. The paper certaintly presents a very interesting view. Part of it is an extension of Heisenberg's work on unified QFT, that the mass originates from self-interaction...

So I was thinking about getting some textbook for self-study GR. I don't need to master it, I just wanted to get a look at it for the first time. Is there a particular textbook that anyone would recommend for me? Thanks!

As I try to understand GR, I find coordinate transformations just about everywhere. My question is simply: What is the reason coordinate transformations play such an important role in GR? Thanks.