Gr Definition and 952 Threads

So, this has really stirred my interest. To be clear, I'm not citing these as sources, simply linking for discussion; An article on the subject, And the abstract. Talking about this elsewhere I seem to find no shortage of objections. But to me it seems fundamentally pretty sound. One...

Do I need to worry about the pore size, or can I just assume that any/all paper filter will remove the organic compound while letting the smaller HCl molecules through? The molecular weight of the organic compound is listed as "240"

A couple of questions about this paper, which, unfortunately, I can't access in is entirety http://link.springer.com/article/10.1007%2FBF02923262#page-1 1) Re: optical coordinates. From what I've read (here and some other sketchy sources), these are similar to fermi-normal coordinates, but...

Homework Statement Suppose that the velocity of an observer O' relative to O is nearly that of light, |v|=1-ε, 0<ε<<1. Show that the Lorentz contraction formula can by approximated by: ∆x≈∆x'/√(2ε)Homework Equations Lorentz contraction, ∆x=∆x'/γThe Attempt at a Solution I think it should be...

8) Use each trigonometric ratio to determine all values of Θ, to the nearest degree if 0°≤ Θ ≤ 360°. c) cosΘ = -0.8722 So, this is what I did for this question: Θ=cos^-1(-0.8722) Θ = 151° This is correct, according to the textbook. However, it also gives another answer: 209°. How do you get...

I have been reading GR but I have these gaps in understanding. Can someone help clear them? 1) SR has a transformation to new co ordinate system that is a linear one. When GR is described, the textbooks mainly discuss Geodesic and distance but I ave not seen the transformation from old to new...

GR can be used to show that the predicted time dilation on the surface of a planet equals the time dilation required by SR at that planet's escape velocity. Can it also be used to independently calculate the mass increase at that velocity without any reference to SR?

So this thread has been closed and I can't comment on it. I am working on this question as well and am stuck on b). I managed to solve for a) and c) but I have no idea how to go about finding the force normal and do not know where the formula "Fnet= mg + ma" came from or why to use it. Could...

Hi guys I need a good introductory Textbook with full solutions on Quantum Field Theory and General Relativity I am an upper level undergraduate. Please pick ones that have solution thanks.

Suppose that you have a region of space with no fields and the only matter is in the form of a cloud of point-masses. On the one hand, within the cloud, the stress-energy tensor vanishes almost everywhere (except right at the point-mass, in which case it is infinite). So the Einstein tensor...

My question is the following: Have there ever been any experimental tests of the Einstein equation (a.k.a. Einstein field equations) for the case of non-vanishing energy-momentum tensor? If so, which ones? I know there's a wikipedia article about tests of general relativity and I have...

Dear, If i start from the Einstein Hilbert ACtion and apply the usual Noether rules (as we use them on flat spacetime ie treating the metric tensor g_munu as any other tensor assuming the existence of another hidden tensor eta_munu describing a flat spacetime non dynamical background, though...

What is the gravitational binding energy in GR in the spherically symmetric case? I calculate ##E=mc^2(1-\frac{1}{\sqrt{1-\frac{r_s}{R}}})## where ##m## is the mass of the body, ##r_s## is the Schwarzschild radius, and ##R## is the area radius as in the Birkhoff theorem.

I think that is a fundamental question of why we need Tensor when dealing with GR? Quoting from the textbook (Relativity, Gravitation and Cosmology: A Basic Introduction) Tensors are mathematical object having definite transformation properties under coordinate transformations. The simplest...

The title says it all, really. Are we able to describe GR in terms of a Graded Time Dilation Field in Euclidean space? From http://cpl.iphy.ac.cn/EN/Y2008/V25/I5/1571 we can see that light curvature can be analogously described via a material with a graded index refraction, so my question is...

Hello friends , I have some conceptual problems in understanding the difference between Minkowski spacetime and the spacetime of general relativity. The general spacetime of GR is defined as a smooth manifold which is locally like Minkowski spacetime . What does this statement mean ? Does...

Bit confused regarding how non-inertial frames can be treated in GR (and by non-inertial i mean affected by some kind of four-force). Can anyone give a brief summary or link to some good sources?

In classical mechanics you want to calculate the moment of inertia for hollow & solid: lines, triangles, squares/rectangles, polygons, planes, pyramids, cubes/parallelepiped's, circles, ellipses, parabola's, hyperbola's, sphere's, ellipsoid's, paraboloid's, hyperboloid's, cones & cylinder's...

I want to study GR from a mathematical point of view but I know almost no physics. Is this possible? And what textbook would be more geared towards this? Also, what are the math prerequisites that I need? I have studied up to analysis on manifolds, some linear algebra and multi-linear...

I'm trying to find examples of stress-energy tensors from exact solutions of the EFE corresponding physically to matter-that leaves out all vacuum solutions(including electrovacuum and lambdavacuum) and pure radiation(null dust)-, I'm finding hard to find any other than the usual SET from...

I have a pretty basic question - one that should have occurred to me long ago, but I never really thought about before. We all know how the effects of gravity are described by the curvature of spacetime - rubber sheets and all that - as well as the equivalence of inertial and gravitational...

Let's say we have a mass with an object orbitting with constant speed in a circular orbit and a distant observer Bob. According to Bob's coordinate system, the orbit is circular at a speed v and a constant inward coordinate acceleration a. The coordinate acceleration is just what is inferred...

Besides the dimensionality (4 vs. 3), how would you go about explaining the difference between tensors in GR and in continuum mechanics? I was asked by an engineer friend that finds GR too "esoteric" and complex to get into.

I never seen any intuitive interpretation of the LHS of the equations. I realize the question is a tall order. But i think something can be extracted. ----------------------------------- *Is this statement correct? The true information content of GR is : 1)The non covariant law of...

One well-known effect of a gravitational source in GR is that it bends space (which has the effect of doubling the deflection of a light ray passing the sun compared with Newtonian gravity). One way of thinking of this bending is that it maps a tangential plane as seen by a local observer...

Hi everyone, I don't fully understand what is the regular method to state and solve problems in GR when no handy hints like spherical symmetry or homogeneity of time are assumed. If I find myself in arbitrary reference frame with coordinates x^0, x^1, x^2, x^3 the meaning of which is unknown...

The Hulse-Taylor (PSR B1913+16) binary pulsar 'observed vs. predicted' orbit decay is one of the great validations of GR. The orbit decay over the recording period of 30+ years is very close to GR prediction as per predicted energy loss through gravitational waves. Hulse-Taylor experiment is...

Does inertial motion (understood in the SR sense) exist in a curved spacetime?

So in special relativity we have ds'^{2}=ds^2, which is another way of saying \Lambda^{T}\eta\Lambda=\eta. Where \eta=diag(-1,1,1,1). It seems in GR the symmetry group for transformations is GL(R,4) or Diff(M) depending on who you ask...

Would there be a direct proof of the energy-stress tensor of general relativity? My lecturer only provides me with a simplified proof - 1. Guess the form of the tensor in special relativity in co-moving frame (ρ+p)uμuv+pημv Note that the pη00 term cancels the p in u0u0, to simplify the...

In various other threads we have been kicking around various equations for a spherical shell and discussing the implications. In this thread I would like to present what (I think) I have worked out about how the shell metric relates to the vacuum metric inside and outside the shell. I hope to...

Hi all, wondering if I might have some advice. I would like to study for a PhD in GR. First things first 1. What would people recommend as a complete book on GR? By complete I mean one that serves as an intro then goes above and beyond, ideally no more than £20! 2. Does anyone have any...

I need some help with a derivation in GR. The linearized field equation in GR is: G_{ab}^{(1)} = - \frac{1}{2}{\partial ^c}{\partial _c}{{\bar \gamma }_{ab}} + {\partial ^c}{\partial _{(b}}{{\bar \gamma }_{a)c}} - \frac{1}{2}{\eta _{ab}}{\partial ^c}{\partial ^d}{{\bar \gamma }_{cd}} = 8\pi...

In SR there is a whole family of so called inertial observers that are defined as those observers that move at relative constant speed with respect to one another, whose descriptions of nature are all equivalent and whose spacetime coordinate are related by Lorentz transformations i.e. those...

Is it possible for parts of GR and SR to be wrong even thought there are things about them that seem to be undeniable?

What is a good book on alternative theories of Special and/or General Relativity?

I wondered anyone can explain the significance of the above as applied to metrics in the context of general relativity. This came up when the video lecturer in GR mentioned that r for example, was null or this or that vector or surface was null, say in the context of the eddington finkelstein...

I just read the following definition of a clock in GR: "A clock is a smooth embedding γ : t → γ(t) from a real interval into M such that the tangent vector \dot{γ} (t) is everywhere timelike with respect to g and future-pointing. This terminology is justified because we can interpret the...

At page 234 in Landau and Lifshitz' Classical Theory of Fields the proper time element is defined through the line element by ##ds^2 = c^2 d\tau^2##, then for a stationary observer, setting ##dx^i=0## for ##i=1,2,3##. One then obtains the relation $$c^2 d\tau^2 = g_{00}(dx^{0})^2.$$ He then...

This has bothered me for some time. In the ADM formulation, we foliate spacetime into 3+1 dimensions by creating 3 dimensional hypersurfaces via ##T = constant## along the worldline of some observer whose proper time is ##T##. This allows us to write dynamical equations for the evolution of some...

My first of many GR questions :cool:: If electromagnetism can be incorporated into the standard model, where I think of electromagnetism as derivable from an action principle ala Landau-Lifshitz, at what point does this process stop working when you use gravitation? I was thinking the...

It seems like Zee lost a trace in his new GR text, but I am sure it is me confusing things. First, he establishes: log\: det\: M = tr\: log\: M Then, differentiating: (det\: M)^{-1} \: \partial (det\: M)=\partial (tr\: log\: M)=tr(\partial\: log\: M)=tr(M^{-1}\partial M) Then he applies...

If time is constantly moving the direction of increasing entropy and quantum systems are time symetric then how do macropscopic entanlged systems such as bose-einstein condensates relate temporally to themselves and larger systems of which they might be subsets? Because BECs are large enough to...

Here is an anecdote about Arthur Eddington: So Eddington thought only he and Einstein understood GR, at some point in history. My question is: did Eddington not realize that David Hilbert was able to derive the Einstein Field Equations before Einstein was? Why did Eddington not feel that...

In order to understand how related are the theories of General Relativity and Electromagnetism, I am looking at the electric and magnetic parts of the Weyl tensor (in the ADM formalism) and compare them with the ones from Maxwell's theory. I have tried to look at the Poisson bracket, but the...

Can someone explain what the expansion, rotation, and shear of a time-like congruence are physically?

The main problem is when we say a manifold is curved surely this is a relative concept - curved relative to what? I've looked at lots of threads asking similar questions and the answer which keeps coming up is that you can tell if a manifold is curved if you are within that manifold, for...

Most of the fundamental equations of nature happen to be *linear* partial differential equations... This includes Maxwell equations and the Dirac equation (don't know about QCD field eqs). On the other hand, the gravitational field equation of general relativity is a nonlinear PDE. As far as...

I understand that SR and GR should not be dependent on the coordinate system. But does GR depend on the existence of a manifold? As I recall, GR is formulated with a metric tensor. And tensors are only defined on manifold. Or is there a manifold independent GR?

I would like to get some foundational concepts straight about GR as it is currently understood (I guess it is not seen exactly the same it was almost a century ago even if the basic concepts remain, this I would like to elucidate here too). For instance, I understand that a basic axiom of GR as...