Gr Definition and 952 Threads

So I've been trying to find an equation that will represent total time dilation. I've looked through a couple threads and it seems the consensus of the threads I've seen on the topic say that total time dilation is the product of time dilation due to velocity and gravity. But I'm not clear...

"Opposite side" of GR I am trying to consider kind of "opposite side" of GR. Let's consider some area in space where density of matter is less then average density of matter across the universe and in every direction average density of matter can be viewed as being higher than at this...

Find the Euler – Lagrange Equation when L = -1/2 (D_p a_u)(D^p a^u) \sqrt{-g} dx^4 Use g_u_v to raise/lower indices D_p is the covariant derivative I am very new at this notation and am having a lot of trouble getting anywhere with this. I know I have to take the action: S = \int Ldt...

Einstein-Hilbert Action --> GR is a saddle point? [Clarification: I'm not claiming GR is wrong or anything. I'm asking if there are issues in interpreting GR as an action principle, and since I assume not, why not?] We can get the equations of GR from the Einstein-Hilbert action by finding...

Which is not homourous but philosophical.

If a theoretical single photon followed a geodesic toward a large mass in space, I understand that the wavelength would shorten as it approached the mass. How would the energy be conserved within the photon, because the frequency must surely remain the same?

how easy does it become to learn general relativity after a good course in continuum mechanics?

I would like to have a conceptually better understanding of GR solutions in the absence of matter, and a little difficulty I usually run into is that seemingly since in these solutions we have both the Einstein and stress-energy tensors equal to zero (which is what it means to have no...

The problem is to calculate the precession of Mercury using a naive approach: {{d(\gamma m \vec v)} \over {dt}} = {-GmM \over {r^2}} So apparently a Lagrangian of the form - mc^2 \sqrt {c^2 - \dot r^2 - r^2 \dot \theta ^2 } - {{Gmm} \over r} gives us a Lagrangian that obeys the previous...

I've been trying to organize my thoughts about conservation laws in GR, and so far I'm not having as much success as I'd like in bringing order to the whole topic. Maybe this is just the way GR is -- conservation laws don't play their usual central role, and their behavior varies on a...

What are the actual problems of joining these two theories? (I've heard various people say that the equations 'fail' or 'blow-up', but I want to know exactly what happens...)

GR with Riemannian (++++) metric? Neither the Einstein field equations nor the Einstein-Hilbert action requires pseudo-remannian metrc. Is there anything interesting about GR with Riemannian metric? Are there still black holes? Also, is it possible to find a solution to GR in which the...

Hi all, I'm posting this here and not in the Beyond the Standard Model forum because my question is not very precise and I don't know anything substantive about strings or LQG. That being said I will launch into my inquiry. It's my understanding that the need for a theory beyond the...

The Wikipedia article Metric tensor (general relativity) has the following equation for the metric tensor in an arbitrary chart, g = g_{\mu\nu} \, \mathrm{d}x^\mu \otimes \mathrm{d}x^\nu It then says, "If we define the symmetric tensor product by juxtaposition, we can write the metric in...

Hello all I am trying to teach myself general relativity and am working through the text 'a first course in general relativity' by Bernard F Schutz. So far I have made slow but consistent progress but I am perplexed by a couple of things in the fluid mechanics part where it derives the...

I just had a strange thought: In section 23 of his popular book, "Relativity - The Special and General Theory", Einstein explains why a clock on the edge of a rotating disk will run more slowly than one at the center, and then says, "thus on our circular disk, or, to make the case more...

There is a great resume on dynamics of thin shells in GR: Berezin87: Dynamics of bubbles in GR (Phys. Rev. D 36, 2919) In section III/A above the equation (3.1) there is the following statement: "Thus, for given inner and outer metrics sigma determine the global geometry (i.e. how the...

causality in GR (was "Is event sequencing relative?") The recent thread on causality, titled "Is event sequencing relative?," has gone in two directions, one discussing frame-dependence of time-ordering in SR, and the other discussing causality in GR. The SR posts were much more voluminous than...

Hi, everybody I'm just wondering what it takes to understand general relativity? And can one understand the underlying math-bench and is it possible to construct intuitive meanings to the concepts of general relativity in a way that is fruitful to its understanding? anyone knows such...

....This is just a concept I have been playing with for awhile... As my knowledge of GR is limited and my knowledge of Mach's principle is limited to its application to inertia I am going to use my own generalizations from them both. If my understanding or interpretation of either is wrong...

Has it ever been demonstrated convincingly that supergravity gives you GR in the continuum limit (as opposed to just some massless spin-2 field)? Where can I find a readable derivation of this fact?

I am wondering if, in general relativity, there is a way to make sense of a statement such as, "the spaceship is 100km from me." In special relativity, we could define this (as long as I am an inertial observer) by choosing global coordinates (t,x1,x2,x3) corresponding to my notions of time and...

I would like to know if anyone who had a good introductory GR course would mind sending me the scanned lectures notes if this person has them. I think textbooks have too many words and I prefer to study lecture notes. I am sorry if this was not the correct place for my post.

Is it possible to deifine local inertial frame which is Poincare invariant (in general relativity) (every manifold is locally flat, so we can chose coordinates which are almost pseudoeuclidean, but in what sense they might be Poincare invariant) Thanks.

I've been trying to get a sense of the differences b/w Newtonian gravity and GR. One thing I was curious about. I'm reasonably certain that Newtonian gravity predicts that two objects of the same mass, but different densities, exert the same gravitational force on a given object at distance R...

I was just reading the old document by H.A. Lorentz " The Einstein Theory of Relativity" which is freely available in ebook and text format. I find it interesting to read some of the comments from those times, and Lorentz provides a nice summary of the thoughts of the days soon after a second...

Hi Can someone suggest a book along the lines of "space-time physics"(wheelerand taylor) which gives conceptual clarity to study (self) along with Schutz GR Thanks

I was just curious as to how someone could find a Quantitative answer out of the equations for general relativity. I've tried to mess around with stuff related to tensors and manifolds but yeah, I can only compute so much given my foundation. In an attempt to build and forge that foundation I...

Homework Statement The point A(2,4,5) is reflected in the line with equation r = (0,0,1) + s(4,2,1) , sER, to give the point A'. Determine the co-ordinates of A'. Homework Equations 1. The equation of the line (parametric equations) 2. A (2,4,5) Dot Product, and distance from a point...

Can anyone point me to a good source using the Schwarzschild metric that gives Einsteins predicted result of the measurement in Principe?

HI, could someone please suggest me a good book to learn both Tensors as well as General relativity? It has to be introductory.

I will eventually learn both, but as far as mathematics goes (not concept,) which is easier to learn, Quantum Mechanics or General Relativity? I really am asking in terms of mathematics, because I know Quantum Mechanics has more application but I am not using that as a factor. thanks!

The thing we call dark matter its really just dark gravity. we don't know if its matter or something else, for example: -in ST it could have something to do with parallel universe -in QM maybe some quantum fluctuation in the higgs field -in GR it some matter that doesn't interact with...

Ok , so I'm already thinking of my gr 12 physics project for next year. We have to build a device anyhting that shows amazing physics principles, does anyone have ideas on what i should build and the physics behind it. Here is the project handout and outline: Overview The main objective of...

Question regarding GR and the "cylinder condition" Im reading that in Kaluza-Klein theory, the derivatives (of the metric g_{\mu\nu} with respect to the 5th dimension, X^4 , were chosen to be zero, to explain why we do not "feel", or detect, the existence of X^4 i.e. the Cylinder Condition...

I've always admired the way Einstein approached gravity, -which had previously been treated as an a attraction, that is, a determined kinematics that had to be accounted for by a force-,from a completely different point of view, looking at it as the curvature that matter-energy produces in the...

The wikipedia article titled "Geodesics & General Relativity" opens with: "the path of a planet orbiting around a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space." Uhhhh... "Real" spacetime has four dimensions - 3 space; 1 time...

Im learning the cartan formalism of doing quick computations of the christoffel symbols and curvature however my book is a bit vague (McMahon). Does anyone have any lecture notes or webpages that do a good job? thanks

What I'm actually trying to find is: The metric for a massless string coming in from +infinity on the z axis, holding a spherical mass (with angular momentum) a fixed distance from the origin, along with another string coming in from -infinity on the z axis also holding a spherical mass. In...

I have always thought that GR was identical to classical physics in the Newtonian limit. In the Newtonian limit one can define an energy density for a gravitational field parallel to the methods used to derive the energy density of a static electric field, resulting in a formula energy...

Hey everyone, I am new to the forum and have a question on the logic of General Relativity. Correct me if I am wrong but my understanding is that according to Einstein's equivalence principle: 1) Freefall in gravity is the same as weightlessness in sufficiently small areas (so an...

or not

What is the symmetry group of manifold which models our world in general relativity. In special relativity this group is Poincare group. Its elements preserve standard lorentz inner product. What structure is preserved by elements of symmetry group in GR (sygnature of metric, maybe sth else?).

http://golem.ph.utexas.edu/category/2010/03/an_invitation_to_higher_gauge.html#c032039

What is a definition in GR that correctly captures the concept that a frame is rotating? Is it enough to say that it's stationary but not static?

I am reading the book The Early Universe by Kolb and Turner and found the following: "In the strictest mathematical sense the universe cannot be in thermal equilibrium, as the FRW cosmological model does not possesses a time-like Killing vector". It is just a matter of calculations to show...

Hello all, In the book "A First Course in General Relativity" by Schutz (1985 Edition) in chapter 2 there is a problem concerning summation that has me confused. Note: This is not homework, just an interest of mine. The given quantities are: A = (5,0,-1,-6) B = (0,-2,4,0) C = [ 1 0 2 3...

Can you help me on making such list? "list of required branches of mathematics to study GR" I'm a high-school student, and I need to know what exactly I must study first to begin studying GR. thanks in advance :)

Hey, I'm new here, so I hope this hasn't already been posted, but I really need help with this question. There is a commonly used example to show how Einstein helped prove General Relativity through space curving due to different ratios in radians of a spinning wheel made to spin at the velocity...

I'm not sure if this has been discussed before. We all know about the Monkey Hunter Demonstration. Assuming a uniform gravitational field, a projectile shot directly at a target will strike the target as long as the target has zero velocity at t=0 and both the projectile and target begin...