Gr Definition and 952 Threads

Dear Experts, I am looking for the variation of magnetic permeability of the plain carbon steel wire grade 1000 to 1095 with respect to the ambient temperature ranging from -40 deg C to 200 deg C. Any leads will be appreciated. Thank you!

Hello everyone, here I come with a question about inertial frames as defined in General Relativity, and how to prove that the general definition is consistent with the particular case of Special Relativity. So to contextualize, I have found that one can define inertial frames in General...

It is commonly said that if you lift an object above the Earth it gains potential energy equal to mgh (m=mass, g=gravitational acceleration, h=height), suggesting that the potential energy is in the lifted mass. This cannot be. Consider the case of two perfectly rigid spheres, isolated in...

Since in GR and SR the basis vectors are generally orthogonal, how can we take derivatives of position with respect to time? For example, the current four-vector is $$J^{\alpha} = \sum_n e_{n} \frac{\partial x^{\alpha}}{\partial t} \delta^{3}(x - x_{n})$$ where n labels the n-th particle. In...

GR lacks absolute space, but does Newtonian physics also? If not what does GR lacking absolute space mean? I had thought in Newtonian physics that there existed an absolute space in which Newton's laws are true, and that an inertial frame was a reference frame in relative uniform motion to...

Imagine three marbles A, B & C with each with 2 small lasers attached. All in the same rest frame, separated from each other by a light year, and forming an isosceles triangle (where AB and AC are the same length, and the centre of BC is a kilometre from A), and that the lasers of each pointed...

Imagine a situation in which a space time curvature propagation reaches a zone (in space time) which it had no prior influence. Would the measured motion (for the objects in that rough zone) in spacetime (subsequently) be unaffected by the changes in spacetime curvature? If the answer was "yes"...

Homework Statement Hi I am stuck on a small algebra set in the weak limit theorem to recover Newtonian equations The text I am looking at: ##\frac{d^2x^i}{ds^2}+\Gamma^i_{tt}\frac{dt}{ds}\frac{dt}{ds}=0## (1) ##\Gamma^{i}_{tt}=-1/2 \eta^{ij}\partial_{j}h_{tt} ## (to first oder in the...

It's one of the most important works in science of all time. It's at least as important as evolution theory and the theory of the atom. Kids these days spend too much time memorizing different types of minerals, and other random scientific facts. Obviously they would not know what a manifold...

I understand that in a 2-body system a circular orbit is gravitationally stable in General Relativity. In Newtonian dynamics, an elliptical orbit is also stable, but is this also true in GR? I understand that the orbit precesses, but I do not intend that to change my meaning regarding stability...

Edit: I mean a new concept as in new with regards to the century before. I'm aware that lorentz and maybe others had some idea even before GR So time slows down for the individual under a stronger gravitational field than for an individual under a weaker gravitational field. But why does this...

Consider the action of a massive scalar field minimally coupled to gravity, that is, $$S = \int d^4x \, \sqrt{-g} \, \left( 2\kappa^{-1} R + \partial_\mu \phi \partial^\mu \phi - m^2 \phi^2\right)$$ The theory I consider is canonically quantised gravity, with ##g_{\mu\nu} = \eta_{\mu\nu} +...

I'm a 20 years old student in the first year course to get a bachelor degree on physics. My question is: is it ok for a person like me, frequently getting into trouble when studying some advanced topics on Quantum Mechanics or General Relativity? In my course, we are learning about basic...

That the metric tensor is not uniquely determined by the EFE and what this might entail has been a source of debate for about a century. A way to view the problem is to decide what the manifold that has the property of diffeomorphism invariance and background independence exactly is in the...

I know that motion equation in field theory deriving in GR is not uniquely.How do we solve this ambiguousness of QFT in curved spcetime?

I'm currently taking a course in Theoretical Mechanics, which is a prerequisite to General Relativity, which I'm very much looking forward to taking. However, I'm not that good in mechanics, and Real Analysis seems to be more straightforward than even the first course in Mechanics. I'm quite...

The differential form of a function is \partial{f(x^1,...,x^n)}=\frac{\partial{f(x^1,...,x^n)}}{\partial{x^1}}dx^1+...+\frac{\partial{f(x^1,...,x^n)}}{\partial{x^n}}dx^nIs there (especially in General Relativity) differential of higher orders, like \partial^2{f(x^1,...,x^n)}? If so, how is it...

Hi, I am a Physics graduate and I am VERY mathematically inclined. (This does NOT mean I know a lot of math. My curriculum focused on experimental physics - which left me with a very keen desire to study all the mathematics involved - so I do need to start from scratch.) I would like to study...

I have no college degree or any advanced formal training in physics, so this may be really, really obvious. Please be kind. In GR, the amount by which time slows down on the surface of Earth compared to "empty" space is: SQRT(1-2GM/(RC^2)). For the surface of Earth that's 6.96 E-10 seconds...

Relativity say as an an object accelerates, time dilates and distances contract. It is my understanding that the shortest distance possible is a Planck length, so as distance contracts, does the number of Planck lengths decrease, or does a Planck length get shorter? It would seem the former...

Hello, I would like to better understand the geometric evolution of a gravitational field of a simple point mass as the velocity difference between two different inertial frames approaches the speed of light. I would also then like to extend into more complex scenarios such as charged...

In gauge theories, the counterterms in the equation to balance the gauge freedom (like the phase in electrodynamics) produce the forces of nature. In GR.. what is the equivalent of the counterterms and what is the equivalent of the phase or isospins freedom in electroweak)?

Consider a 4 current J^\mu and a metric g then conservation laws will require \del_\mu J^\mu = 0 my lecturer gave me a brief problem and I think I'm missing some understanding of it he writes What I'm not understanding is, where he states, if we choose B to be the time slice between etc...

This paper offers a Nobel laureate perspective on the history, status and future of GR in the astrophysical regime - https://arxiv.org/abs/1609.09781, General Relativity and Cosmology: Unsolved Questions and Future Directions.

I know that in Special Relativity, proper acceleration is understood as: a*ga^3, where ga is the lorentz term and 'a' is coordinate acceleration. Is there a corresponding expression for proper acceleration within the various geodesics that result from solutions to Einstein's Field Equations? If...

Which book among Bernard Schutz , Stephani and d'Inverno is the best for an introductory level approach to GR ? I have read some tensor analysis from d'Inverno and have not found its treatment rigorous enough .

I wonder what really motivated Einstein to formulate his general theory of relativity: a) would be due to the principle of equivalence? b) it would be because after the relativistic formulation of Maxwell's equations, there was only the classical gravitation with the factor 1 / r ^ 2? c) would...

9/1/2016 Orbital mechanics Wikipedia, the free encyclopedia This reference states: "General relativity is a more exact theory than Newton's laws for calculating orbits, and is sometimes necessary for greater accuracy or in highgravity situations (such as orbits close to the Sun)". Can GR...

Let me start by saying that I'm a physics student but I have no experience with GR other than some pop-sci and some clarifications on that pop-sci from various sources, so basically I'm saying that some math is fine but please bare in mind that I have no real experience with the relevant math...

Hello all. I am self teaching physics, and after completing Classical Mechanics (Special Relativity included), Classical EM and an introductory course to QM, I would like to take a very introductory look to General Relativity. With this purpose in mind, I have chosen 2 books, and I would like...

Book: Landau Lifshitz, The Classical Theorey of Fields, chapter 11, section 95. I have gone through the derivation of Einstein field equations but not without holes to fill and fix in my understanding. Let's start with the action for the grtavitational field ##S_g## which after some explanation...

Im curious what is it about space-time or Einsteins field equations which explains Mercurys precession correct while Newton's formula doesn't? So exactly what difference causes GR to explain it that Newton could not?

Momentum constraint in GR in ADM formalism is written in the form $$\mathcal M_i=\gamma_{ij}D_k\pi^{kj},~~~~~~~~~~(1a)$$ or equivalently $$\mathcal M_i=D_k\pi^{k}_i,~~~~~~~~~~(1b)$$ where ##\pi^{ij}=-\gamma^{1/2}\left(K^{ij}-\gamma^{ij}K\right)~##, ##K=\gamma^{ij}K_{ij}~##, ##\gamma=\det...

I want to ask this in the Relativity forum but thought there are more quantum experts here. So most of you Bhobba, Neumeier, etc believe the world is really classical and all the quantum things are just for calculation purposes or aids. Can you take the analogy to General Relativity? Can we say...

I am hoping someone can clarify some confusion I have. It is my understanding that there is no such thing as absolute velocity or acceleration in GR. If one observer is moving near the speed of light and the other is stationary each observer will see the other as in motion. But if they each...

Is it fair to say, when talking about spacetime with a given metric, it would be redundant to state that the associated set has the metric topology placed on it. In other words, let ##M## be a set, ##O## the metric topology, ##\nabla## a connection, ##g## a metric, and ##T## be the direction of...

So we know that in GR electromagnetic waves have their trajectories effected by the gravity of stars and planets. But how about gravitational waves. Are their trajectories altered by gravity? If so, would this imply that gravitons are self-interacting if they exist?

Where can I find a derivation of the vacuum solution for GR directly from the Riemann tensor of zero trace, i.e., Weyl tensor, instead of the more traditional Schwarzschild derivation?

We have been searching for Dark Matter a long time, is it time to look at theories like this Galileon one? What draw backs does it have? arXiv:1607.02606 [pdf, ps, other] No need for dark matter in galaxy clusters within Galileon theory Vincenzo Salzano, David F. Mota, Mariusz P. Dabrowski...

Is it possible to explain themain ideas of GR without complicated math? In particular, what is the relation of current model of universe (FLRW) and GR? what is the difference between spacetime and universe, spacetime is surely curved and universe can by flat at same time? both mass and energy...

I think this should be equal to the famous precession angle, but with a negative sign: ##d\phi = 6\pi m/r## correct?

Hi. There were theoretical (find transformations under which Maxwell's equations remain invariant) and experimental (speed of light is constant, Michelson-Morley) indications that made the development of SR inevitable. But what about GR? Was there a "need" for this theory or was Einstein just...

Ok. I get that objects seem to fall because of curved spacetime, when they're actually just moving in straight paths. I get the example of ants walking in straight lines on the surface of a sphere, thinking that something attracts them to each other. What I don't get is how the "ants" are...

http://arxiv.org/abs/1105.3735 I have a question about the paper that haushofer mentioned. In the paper, the author states that Moving on to helicity 2, the required gauge symmetry is linearized general coordinate invariance. Asking for consistent self interactions leads essentially uniquely...

In explanations of the importance the tensors I often see people refer to transformation properties, general covariance and the like. Now, I have also often read that in principle any physical theory, e.g. classical mechanics and special relativity, can be written in a generally covariant form...

Hi, When I started learning about GR I wondered if it emerged from SR (which the name suggests) or if the connection between the two is mere technical. GR describes the behaviour of the metric of space-time, which is locally Minkowskian and therefore SR applies. But is a curvature-based theory...

In view of the observational equivalence of gravity and acceleration, does acceleration produce ripples in spacetime, similar to gravity waves?

I'm trying to do past exam papers in GR but there are some things I don't yet feel comfortable with, so even though I can do some parts of the question I would be very happy if you could check my solution. Thank you! 1. Homework Statement Spacetime is stationary := there exists a coord chart...

(precursor: I have not formally studied GR) I have noticed that the gravitational constant found in classical gravitation is also used in GR. Why is this the case? Am I correct in thinking that the constant was determined by Cavendish and was for the classical theory of gravitation? So, my...

My professor is mentoring me through learning GR over the next year with the goal of doing research with me in the long term in the field. I need to pick up a few things along the way. The summer is going to be spent mostly picking up the necessary material for jumping into Carroll's book, and...