General relativity Definition and 999 Threads

The metric $$ds^2=-R_1(r)dt^2+R_2(r)dr^2+R_3(r)r^2(d\theta^2+sin^2d\phi^2)$$ when changed to $$ds^2=-R_1(r)dt^2+R_2(r)(dr^2+r^2d\Omega^2)$$ upon setting ##R_2(r)=R_3(r)##, the later metric holds the name of isotropic metric. My question what is the difference between the first and the second...

Hello, I'm not an Academic, I love physics as a casual hobby. So I have few questions that stuck in my mind. Here is the first one: By Einsteins General Relativity everything including us stuck to Earth by gravity. Earths mass bends the Spacetime. The gravity means: deformed space is pushing us...

So, it always (at least in the books that I have read or scanned) that the Einstein-Hilbert action $$S=\int{\sqrt{g}d^4xR}$$ is directly posed without an explanation of its origin. My question is how did it occur to Hilbert or Einstein to write down this specific form of action?

I'm about to start my senior year at university pursuing a double major in physics and electrical engineering. I decided recently that I wanted to go to graduate school for physics so I started thinking about the area I would like to specialize in. My current university does most of its research...

What impact has Eduard Prugovecki's work in QGR have on nowadays research?

Equivalence principle says that gravitational forces are equivalent physically to inertial forces. Can someone explain what is meant by that and how was it concluded?

It took einstein 4 years to complete his general theory of relativity but the fundamental idea behind this work is that he believed that space is curved , how he is sure about this idea from the beginning ?

If R is Ricci scalar ∇i∇j F(R) = ? , where ∇i is covariant derivative.

There is a rumor going around that a gravitational wave inspiral has been seen at advanced LIGO. The web sites say it went on line in Sept, 2015, so I guess this is possible. Has anyone here heard anything?

Just as a fore-note, I understand this question may be hard to answer, and I'm sorry if I slip into philosophy. We humans can understand time on our scale, but we cannot necessarily comprehend events that occur say on a quantum level, they seem to go to fast. Now my question that arises is that...

Hello everyone, I'm a senior undergraduate and I'm planing to do a Monograph related to Quantum effects in Gravity (Hawking radiation or something similar(?)) or even some QFT in curved space-time (maybe ambitious since I know this is VERY HARD and I don't have much time), the thing is I can't...

Dear all I am studying general relativity and i have a question as follow. We have the 2- sphere can be scanned totally by a coordinate system (theta, phi) with the metric tensor written in terms of theta and phi. Now i want to divide the 2-sphere into charts 4 charts then each will have its own...

Hi, firstly I wanted to say thankyou for this forum, its provided me with a lot of help over the years and now it has come to that dreaded question that can not seem to poke at at all. I'm in my 4th year and taking General Relativity for the first time, with a hap-dash differential geometry...

I appreciate that this may be the 100th time this is asked but I am yet to see an answer which addresses the question head on. Given that reaching light speed creates both a length and time singularity; both length and time amount to zero for the propagating wave/photon. Why does that photon...

I have an equation that says $$C_1\partial_{\mu}G^{\mu\nu}+C_2\frac{1}{2}\epsilon^{\mu\nu\rho\sigma}\partial_{\mu}G_{\rho\sigma}=0$$ If I want to get rid of the ##\epsilon^{\mu\nu\rho\sigma}## in the second term, I know I must multiply the equation by some other ##\epsilon## with different set...

Hello Physics Forums! Supposing that we have an action that says: $$L=\frac{1}{2}R-g_{C\bar{D}}\partial_{\mu}z^C\partial^{\mu}\bar{z}^D+\frac{1}{4} + \frac{1}{4}ImM_{IJ}F^I_{\mu\nu}\cdot F^{J\mu\nu} +\frac{1}{4}ReM_{IJ}F^I_{\mu\nu}\cdot \tilde{F}^{J\mu\nu}$$ where...

I would like to hear different examples of presenting the difference that general theory of relativity relates between a stretched piece of spacetime around a planet and a not stretched one far away from any kind of mass or energy distortions...these examples i would like to be written in a...

Hello! I am working on homework for my general relativity class, and I am very confused about how to tell the difference between spacelike, timelike, and null vectors, and the book is very unhelpful. Relevant equations Consider two four vectors a and b whose components are given by: a^α=(-2, 0...

How are we, and the universe effected from its accelerating expansion? Also how will our perception of the world around us be effected, since the universe is expanding and light is constant? <-Will things appear to move slower? I know that we only experience just a small fraction since the...

How does one derive the general form of the Riemann tensor components when it is defined with respect to the Levi-Civita connection? I assumed it was just a "plug-in and play" situation, however I end up with extra terms that don't agree with the form I've looked up in a book. In a general...

A useful and concise (36 pages) history of the development and use of GR by one of the established experts in the field is posted today on the physics ArXiv : 100 Years of General Relativity by George Ellis. Garth

I'm studying General Relativity and Differential Geometry. In my textbook, the author has written ##x^2=d(x,.)## where d(x,y) is distance between two points ##x,y\in M##. I couldn't understand what d(x,.) means. Moreover, I am not sure if this is generally true to write ##x^2=g_{\mu\nu} x^\mu...

Hey guys, what do you think about this: Let's put a planet in empty space, on the surface of the planet we put a a guy named Bob, Bob's task is to accelerate the planet by pulling on a provided rope. He must extend his arm, grab the rope and bend his arm at maximum force. Bob's identical twin...

I have a question about the directional derivative of the Ricci scalar along a Killing Vector Field. What conditions are necessary on the connection such that K^\alpha \nabla_\alpha R=0. Is the Levi-Civita connection necessary? I'm not sure about it but I believe since the Lie derivative is...

I'm wondering if time and light(entire spectrum) can only coexist simotanuously. When we look out into the cosmos and see stars they can be many light years away. Because it takes time for light to travel. That may have not been relevant. But what I'm saying is... Time is manipulated by the...

I read in many books the metric tensor is rank (0,2), its inverse is (2,0) and has some property such as ##g^{\mu\nu}g_{\nu\sigma}=\delta^\mu_\sigma## etc. My question is: what does ##g^\mu_\nu## mean?! This tensor really confuses me! At first, I simply thought that...

Homework Statement Suppose v^\mu is a Killing Vector field, the prove that: v^\mu \nabla_\alpha R=0 Homework Equations 1) \nabla_\mu \nabla_\nu v^\beta = R{^\beta_{\mu \nu \alpha}} v^\alpha 2) The second Bianchi Identity. 3) If v^\mu is Killing the it satisfies then Killing equation, viz...

Hi, Apologies; In spite of the numerous excellent threads that exist discussing GR books, I felt compelled to create another one. I'm taking a first course in GR & Cosmology, and am trying to select a textbook as the main 'roadmap' through GR. This is a first course on GR in the UK, which is...

Hello all, first post. I have come here to get second opinions on the program I have written to compute the Einstein Tensor (the Riemann Tensor and Ricci Tensor). I enjoy looking for solutions to the Einstein Field Equations, however computing them by hand is not realistic. I decided to write a...

-- Hi. When a gravity wave pass Earth then the time goes a little faster and/or slower. Can there be a phenomenon in the universe that create a gravity wave that is so curved, that when it pass earth, the time stop or go infinitely fast? Regards Magi --

As far as I understand it gravity is sensitive to absolute energies, as seen directly through Einstein's equation G_{\mu\nu}=8\pi GT_{\mu\nu} Thus the local geometry of spacetime is directly affected by the local energy density (and not just differences in energy). So whenever gravity is taken...

According to Hawking [1] it is posited that light photons at the event horizon of a black hole must cease to move, and remain motionless for the entire lifetime of the black hole. It is also observed [http://dls.physics.ucdavis.edu/~scranton/LensedCMB/a2218.gif] (and calculated) that the path...

What is the exact difference between null geodesics and null curves? Please explain both qualitatively and quantitatively.

FAQ: Can special relativity handle accelerated frames of reference? What is the distinction between special and general relativity?Einstein believed, erroneously, that the crucial difference between special and general relativity was that general relativity allowed accelerated frames of...

Hello guys . Through all the analysis of theory of general relativity we used what so called Manifolds Manifolds as we know are topological spaces that resemble ( look like) euclidean space locally at tiny portion of space And an euclidean space is the pair ( real coordinate space R^n , dot...

So I'm wondering if anyone has personal or anecdotal experience of people making the specific transition from general relativity to an industry job. It doesn't have to use specific math skills from GR, but bonus points if there is some relation. It seems that most of the options are somewhere...

Dear friends, Does anyone know how we can solve the TOV equations for a non constant density? In all the references, I just saw the solution for a constant density. Thanks in advance for the help :)

It is said that matter curves space and space tells how the matter to move. 1. Suppose I am moving in a street and there is lots of matter like houses etc, how that matter is governing me how to move? 2. And why something say a ball falls downhill from a mountain?, ball should stay at that...

How to find gravity of an object, like mirror,glass,tree,house etc using general relativity? Because every object exerts gravity.

Homework Statement I am trying to derive the curvature tensor by finding the commutator of two covariant derivatives. I think I've got it, but my head is spinning with Nablas and indices. Would anyone be willing to check my work? Thanks Homework Equations I am trying to derive the curvature...

Hey all, I'm a math and physics graduate who will be starting math grad school in a little over a month, and, though I know I have time to decide, I'm a bit conflicted about what to concentrate in. I'm broadly interested in the applications of math in physics. Specifically, I've always had...

Hello! I started learning relativity recently and I'm an engineering student. I can't stop drawing similarities between the nature of gravity and behaviour of continuous media in the field of continuum mechanics. Is there some direct connection and if so, has something like this been explored...

From what I have read, it sounds like GR predicts that under certain conditions, space itself will expand. If this is incorrect, please just let me know and ignore the below. While I don’t know the math involved in GR, I can understand explanations of how gravity distorts space-time, to alter...

In his book (Relativity) published in 1920 Einstein said that in General Relativity the speed of light is affected by gravity and therefore isn't a constant: In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of...

I am trying to use the Israel junction conditions for a null surface, but I am running into complications with defining a normal vector for a null surface. As I understand it the normal vector is defined to be perpendicular to the surfaces tangent vectors n\cdot e_i=0, as well as satisfying...

Let f:p\mapsto f(p) be a diffeomorphism on a m dimensional manifold (M,g). In general this map doesn't preserve the length of a vector unless f is the isometry. g_p(V,V)\ne g_{f(p)}(f_\ast V,f_\ast V). Here, f_\ast:T_pM\to T_{f(p)}M is the induced map. In spite of this fact why...

DaleSpam submitted a new PF Insights post Understanding the General Relativity View of Gravity on Earth Continue reading the Original PF Insights Post.

Pretty straightforward question. The Einstein-Hilbert Action says that the Lagrangian for Gravity is ##L=R(-g)^{1/2}## where ##g## is the determinant of the Metric Tensor and ##R## is the Ricci Scalar (Actually I am not sure if the determinant of the metric should be included there). From this...

Hello. Let's consider a beam of monochromatic light (just one frequency). 1. Light creates gravity field. 2. Gravity affects the speed of light. Q1: Are 1. and 2. true? Q2: Does the speed of light depend on the intensity and frequency of the light? Thank you for you time :) Greetings!

Hi all, I'm preparing for my bachelor thesis. I have to study some articles for the mimetic dark matter. But before this my advisor sad to me to study from Landau Vol. 2 Field Theory some General Relativity(it's my first time that I study it), chapters 10 and 11(Particles in a gravitational...