What is Gr: Definition and 952 Discussions

I'm a little confused about certain assumptions usually made in GR as to how rigorous they are mathematically speaking. For instance the assumption generally presented without proof that GR spacetime manifold is a Hausdorff space seems not to be warranted given the fact that pseudometric spaces...

Hi, I am interested in obtaining a FREE mathematica package that can: 1) Calculate standard GR tensors (connections, Ricci, Einstein etc.) 2) take covariant derivatives 3) and define tensors Does anyone know of a good Mathematica package?

There are various roads from SR to GR. In a couple of years I may get a chance to teach a semester-length class on relativity for liberal arts students. Any comments on what story line works best? Some possibilities: (1) Thought experiments with elevators suggest that the Newtonian...

I love Physics! I've been thinking about if... you were in a room with a window, bouncing a ball... and you were looking at another building where you could see a room with a person bouncing a ball, but ... their time was moving at half speed (Caused by gravitational time dilation only ( not...

To avoid hijacking an existing thread, I wanted to start a new one on how "gravitational forces" are represented in GR. There doesn't seem to be a lot on this in the intro textbooks, alas, which mostly deal with the issue by avoiding it. Which suggests there could be some non-obvious...

The title says everything. Can a mathematician do fruitful research in general relativity if he masters differential geometry and manifolds?

Can anyone help me simplify the expression \frac{\delta g_{\mu\nu}}{\delta g^{\kappa\lambda}}? I haven't seen a term like this before and I don't know how to proceed. It seems like it might be the product of some kronecker delta's but I'm not sure.

The problems are Number 12 and 13 on this link http://isites.harvard.edu/fs/docs/icb.topic1096438.files/PS4.pdf I have the value of k for sum number 12, it is 1.54*10^-4. Im completely stuck with number 13 cos I'm unfamiliar with that concept and it kinda went over my head in lecture...

Superluminal Neutrino Breaks SR and GR...? I have reading a lot of articles and editorials about apparent neutrinos that went faster than the speed of light by 60 nanoseconds, I read some that say yes and no, so I'm a bit confused. So is it true?? Are there neutrinos that went faster than the...

When is the first time a student of physics works with Einsteins field equation and does Friedmann cosmology?

I find this passage from A Brief History of Time a bit hard to believe. When he talks about using imaginary time for the purposes of calculation, is it the same like in the Schro eq which uses an imaginary number? How plausible is the following passage? Is using imaginary time a common practice...

I am new to General Relativity, so please excuse my ignorance ahead of time. :) While attempting to grasp the concept of bending spacetime I was stumped by the concept of continual gravitational forces and how they exist in the concept of GR. To clarify I understand the following as...

In SR, Four velocity was the proper time derivative of a world line, do we have to take the covariant derivative instead in GR?

When considering the Newtonian forces, it's somewhat intuitive to think about the equilibration of forces, e.g. two charged particles overcoming the gravitational attraction to repel each other. Nothing new. What puzzles me though is to consider the same case within the context of GR and QED...

I've been searching around this forum and the internet, and I still have a hard time understanding how curved spacetime, as described by General Relativity, can cause us and objects to fall back on the surface of the Earth. I get the concept of Geodesics and how planets revolve in orbit around...

In this thread in another forum, I calculated the coordinate speed of light as measured by a distant observer. As far as I understand it, the length contraction in GR is only in the radial direction, right? None tangent, correct? The time delay of light found, though, trying different examples...

Hello everyone! I'm new on the forum (been browsing threads for some time though) and this post is both an introduction of myself and a first question. I have a huge interest for physics but my working knowledge (having studied it in school, oh well some 15 years ago) is limited to classical...

In GR a object follows a geodesic when free falling as I understand. A object near the sun for instance wil fall to the sun following that line. If the initial speed is different the path will be different. How can it be that the geadesic is depending on the initial speed of the object...

I am trying to understand the expansion of the universe and the implications of distant galaxies receding from us at superluminal speeds. To properly understand how this is not forbidden by GR, I wanted to focus on exactly what it was about GR, what 'rule', that said an object can't travel...

OK, just a bit of fun . . . hope no-one is too offended ;) Inspired by the Newtonian orbit example here: http://www.travisglines.com/tag/runge-kutta, I thought I'd see how much GR I could do in JavaScript/HTML5 canvas. So, I got a side-by-side Newton/Schwarzschild demo going, code here...

I have read over and over in various places about coordinate transformations, and understand the theory (really!), but can't find any worked examples of actual use of the transformation equations. Does anyone know of any web references or tutorials on the subject? To make things a little more...

Theres a good thread over here: https://www.physicsforums.com/showthread.php?t=613210 I don't want to derail it. But if energy is "poorly defined" globally in GR as explained in that thread then let's exploit it. Let's devise a "machine" that creates energy. I pose this in such a...

Hello fellow physicsists! I have some (and will probarbly get more) questions about differential geometry and general relativity which I would like to get answered. Most of my wonderings are usually intuitional errors so pure calculations are rarely needed. Here comes the first one...

Homework Statement I'm trying to grasp how the indices are listed when writing out multiple vector products or divergences or gradients, etc. I'm working with 'An Introduction to General Relativity' by Hughston and Tod.Homework Equations A\wedge B = \varepsilon_{ijk}A_{j}B_{k} [A,B,C] =...

The relationship between space (or spacetime) and matter is giving me some trouble. If the universe was created (all its matter) in a planktime explosion then the force of said matter must be driving the expansion of space itself. I view the matter as pressing against the walls of space and...

Do the GR tensor equations have specific solutions that post-dict the big bang? I have seen references to GR providing a theoretical basis for the big bang. Exactly what is the nature of this theoretical basis? If the mathematics for this is too complex for posting on this forum, I would...

My question might appear simple to a few. As the light observance of Einstein's experiment comes into proposition, I am having a difficult TIME understanding. (No pun intended). Let us start with the basic idea...as I'm sure there are several variations. A man stands in the middle of a...

We know that the reason energy and momentum are conserved is b/c of Noether's theorem...time translational invariance implies energy conservation and space translational invariance implies momentum conservation. Now in a curved spacetime you can still form conserved quantities - energy and...

You always hear that GR and QM aren't compatible, but I've never seen an explanation as to why. If I had to guess I would say it's more than quantum mechanics isn't compatible with GR than the other way around, but I really don't know where the conflicts are.

One of the most frequent questions in this forum is why there is a contradiction between General Relativity and Quantum Mechanics. The most frequent answer is that, in high-energy conditions, some integrals diverge, giving nonsense. I could not find a mention of which integrals one is talking...

Which is more difficult to understand general relativity or Quantum Mechanics. Neil de Grasse Tyson basically straight-up contradicted himself in a docu on Einstein. In the beginning he said, GR is so complex that only a few people can understand it. At the end he said GR is simple, profound...

I decided to track down and read the original article in NYT reporting on Einstein's successful prediction that light would bend around the sun. It was not on the front page but maybe around page 11 or so. You can read it here...

This is from Robert March's book Physics for Poets: How accurate is the above statement?

Forgive ne if this sounds stupid but does GR take into account angular momentum, torsion, and other effects of rotation? The stress energy tensor doeznt appear to have any terns that are meant two accommodate angular momentum abd rotational stress.

Hello, Would you know a reference showing and deriving the equations of light rays in GR. I would like to read that as well as to compare that to the equations of motion of test particles in a gravitaional field. Thanks, Michel

In the context of Friedmann's time, 1922, how did he know to make the metric scale factor, a, a function of time when Hubble's redshifts were not yet published? I understand that he took the assumption that the universe is homogenous and isotropic, but does that naturally imply that the universe...

Literally running out the door, but came upon this. It seems to be a really interesting avenue to test GR vs. other gravity theories using hoped for GW detectors. http://arxiv.org/abs/1204.2585

Which and why do you believe will turn out to be more 'fundamental' (in the sense that one will prove to be the foundation of a theory which goes beyond the SM, while the other will be explained away by it). Or maybe both, or neither?

Homework Statement Consider a 2-dimensional line element: ds^2=x^2dx+2dxdy-dy^2 Raise and lower the indices of given vectors by finding the raised index metric, etc, blah blahHomework Equations V_a = (1,-1) and W^a = (0,1)The Attempt at a Solution Solution is given and I understand how to...

Steve Carlip says this [back in 2007], here,: http://www.2physics.com/2007/06/symmetries-horizons-and-black-hole.html"...Until fairly recently, no one had a clear idea of the microscopic states responsible for black hole entropy. Today, we suffer the opposite problem: we have many...

Remember that the electroweak force couldn't be renormalized for over many decades, until Weinberg and company finally renormalized it when mass was introduced via the higgs mechanism. Right? Now in the quantization of general relativity, we haven't been able to renormalize it after decades...

Hi all, Einstein definitely had to learn tensors from someone else <via correspondence>. But he did not need tensors to intuitively get idea of curvature. So, Can some one share in that simple language, How he got the intuition that space time should be curved in accelerated/...

I've been playing with the idea of seeing how far I can get with general relativity without resorting to the learning of tensor calculus (at one point I decided I wouldn't believe SR until I derived it myself. I did (didn't need much more than 8th grade algebra), came up with the same results...

https://www.amazon.com/dp/0393965015/?tag=pfamazon01-20 How many here own this book by Ohanian & Ruffini "Gravitation and Spacetime"? A review mentions: "Ohanian introduces linearized GR (in a completely logical and satisfying manner) before Riemannian geometry" What's linearized GR...

At the time Schwarzschild derived his solution (1915) he only had a version of the EFE that was not fully coordinate free, he used the equations in unimodular form, and therefore he could only consider the "outside of the star" part of the fully general covariant form we know now. So does a...

In the Physics World article "Loop Quantum Gravity" by Carlo Rovelli, he mentioned that: "General relativity is not about physics on curved spacetimes, asymptotic space–times, or connections between theories defined over different backgrounds. It is the discovery that there is no background...

I noticed a few sources that seem to indicate that Clifford algebra may be used in both QFT and GR. I've seen where the Clifford algebra is a type of associative algebra that generalizes the real numbers, complex numbers, quaternions, and octonions, see Wikipedia on Clifford Algebra. And I've...

I'm not sure if this is the correct place for this as it is not about relativity as a topic in physics but the history of Einstien's theories. Both SR and GR were verified (or, more properly, not falsified) by experiment relatively (pun intended, I guess) soon after the theories were...

I usually don't do threads like this, but I wanted to get some opinions for either people in the field, or people who have at least taken graduate level classes in GR or QM. What are the main math topics in each of these fields? Is there much overlap at all or are the two topics pretty...

I am reading about rotating water in bucket - about Mach's principle. But, how general relativity explains this bucket. 1. Let us say, that bucket with water is the only object in universe. What GR says. 2. Let us say that one star in distance is in this universe. How rotating water "know"...