Gr Definition and 937 Threads

I am exploring the topological reasons behind certain physical constants. In GR, is the factor of 2 in the Schwarzschild radius (Rs=2GM/c^2) ever treated as having a deeper topological significance?

I'm a theoretical physics student working on my master's degree in China and trying to seize the opportunity to study abroad, especially in France. It's so frustrating that I still cannot find a subject or thesis that satisfies both my interests and learning goals. Here's the thing. I major in...

So I've often heard that when GR is applied to the entire observable universe to calculate its curvature, we get a value of zero, meaning that the entire universe is flat. I've got 2 problems with this. The first is that I thought GR was a local theory i.e. it only applies locally. Trying to...

We only measure time via the relative movement of a standard, agreed reference, a clock for example. If we replaced all instances of "time" in the formulation of SR and GR by "relative motion [ie, of an agreed reference]", would SR/GR remain correct/consistent? Or does SR/GR rely on a deeper...

James Hartle has died. A few years ago I had the pleasure of using his text to teach an undergrad GR course.

Hello, Springer books are on sale this week so I wanted to buy some textbooks to support my studies and (eventual) future career. I'm an undergrad (in europe) and my courses next year will be QM, GR and statistical mechanics, so I was looking for books about these topics, but any suggestion on...

Please help me confirm that I understand this correctly. Imagine a system comprised of two black holes orbiting each other, which will eventually merge. At any point in time we describe the stress-energy tensor of the system. Assume that we could solve the EFE's for every point (t,x,y,z). This...

The GR predictions for the universe's size are those of fig.a. Whereas the Hubble expansion is exponential, fig.b. How are the two reconciled?

On p138 of Wald's General Relativity, 4th para, he says: Firstly, I already understand (of course) that this sort of simplification is easy and immediate in Newtonian mechanics, since conservation of angular momentum always occurs in central force problems (the proof is just a few lines) and...

Please, how can I get a copy of this program library?

I am sorry but I can't seem to find the actual estimated value of the cosmological constant that is predicted by quantum field theory. Can anyone help me and tell me the approximation of that value and/or the value of the approximate observed cosmological constant that physicists today think...

Assume you have a two particle system, A, which has a mass and gravitational pull of g, and B, an object with low mass, The system starts at time 0 with the distance between A and B being 0, A being at rest and B having enough kinetic energy to move it a distance r away from A, until time t all...

I read there are 2 degrees of freedom in GR after boundary conditions specified. Does that mean 2 equations are enough for EFE equivalent? Those two seem like the amplitude and a phase.

I guess it is safe to say that SR is, mathematically speaking, a framework that correlates discrete events in spacetime by way of a universal constant (the speed of light) so that the "proper distances" that separate them may be determined. I think this means that every conceivable "instant...

Hello everyone! I was just watching a video, and to my surprise I was able to understand a little about GR (General Relativity). I'm looking to confirm my understanding, and also ask some basic questions. From what I understand in Newtonian gravity the space time is considered to be uniform...

He draws an n-manifold M, a coordinate chart φ : M → Rn, a curve γ : R → M, and a function f : M → R, and wants to specify ##\frac d {d\lambda}## in terms of ##\partial_\mu##. ##\lambda## is the parameter along ##\gamma##, and ##x^\mu## the co-ordinates in ##\text{R}^n##. His first equality is...

On pages 106-107 of Spacetime & Geometry, Carroll derives the geodesic equation by extremizing the proper time functional. He writes: What I am unclear on is the step in 3.47. I understand that the four velocity is normalized to -1 for timelike paths, but if the value of f is fixed, how can we...

Read the bio / fiction chapter on Karl Schwarzschild in Benjamin Labatut’s great Book, and curious on a little color on how he developed the solution - I had thought finding an exact solution in GR was just math chops, but actually any Lorentzian metric is an exact solution, so the difficulty...

Our current model (FLRW) is clear that the universe has a continuous temporal asymmetry. This is seen as the expansion factor grows with time, and thermodynamically with entropy. A continuous transformation in the current model ##t \rightarrow t + dt## is not the same as ##t \rightarrow t - dt...

A new group of investigators are attempting something similar to Deur's work, which seeks to explain dark matter phenomena with general relativity corrections to Newtonian gravity is systems like galaxies. Deur's most similar publication to this one along these lines was: One thing that makes...

Mentors’ note: this thread is forked from https://www.physicsforums.com/threads/free-fall-in-curved-spacetime.1016510/ But what if the gravity field is homogeneous? Like that of an infinite massive plane? The objects in the ship will stay where they are. An infinite massive plane is quite...

I'm a graduate theoretical physics student at the (almost) end of his master's degree with a fairly varied curriculum, as I attended both QFT (and sub-courses on qed qcd etc) and GR courses. However in my latest intro to quantum gravity classes I familiarised with tetrads and, after a lot of...

I know that simulation of phenomena in general relativity is computationally complex. However, simulating the phenomena you are studying often helps. In your opinion, should I study methods to simulate what happens in relativity? Is it worth it? Or would it distract me from the theoretical...

I have been learning gr on YouTube for the last few months. Most of the videos and the book I have focus on high level understanding. I can do all of the tensor calculus proofs. However simple questions like how you set up a velocity vector or measure proper time in schwarzschild are beyond me...

According to Wikipedia, the definition of the Riemann Tensor can be taken as ##R^{\rho}_{\sigma \mu \nu} = dx^{\rho}[\nabla_{\mu},\nabla_{\nu}]\partial_{\sigma}##. Note that I dropped the Lie Bracket term and used the commutator since I'm looking at calculating this w.r.t. the basis. I...

I'm reading the book "Semi-Riemannian Geometry: The Mathematical Langauge of General Relativity" by Newman. There are definitely other questions on math background needed for GR, but my aim is to find which topics from that particular book aren't essential so that self study is more efficient...

Hi, has anyone tried to build "quantum GR", using the expectation value of |Psi(x)> as a "quantum ruler" and |Psi(t)> as a "quantum clock" to build up the idea of a "quantum metric"?

Hello everyone, I know that GR equations are complicated and beyond my scope. But does GR give a simple gravitational equation: Force (as we know it) as a function of distance? (without any complicated tensors). - If yes. What is the equation? Does it give us something similar to Newtons...

Does unitarity have to be obeyed in a full quantum gravity model?

If I had a nickel every time someone depicted curvature of space-time as a marble on rubber membrane I would have a lot of nickels however that description is not accurate; A channel called science clic has the most accurate visualization of bend of space-time I have ever seen however if anyone...

According to general relativity (GR) time runs faster in a weak gravity field relative to a stronger one, for example: clocks run faster at the top of a tall building than at ground level. According to the principle of equivalence the accelerating space elevator should be analogous to gravity -...

In Minkowski space, with line element $$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$$ (and ##c = 1##) we take spacelike trajectories to have ##ds^2 > 0##, null trajectories to have ##ds^2 = 0##, and timelike trajectories to have ##ds^2 < 0##. This makes sense given our definition of the line element...

Any recommendations on introductory math related to general relativity for someone with an engineering background? I've been trying to learn the necessary math, but I'm having a hard time figuring out what I should be studying. Basic background for me is college physics I and ll, all the...

I'm having trouble with Rovelli's new book, partly because the info in it is pretty condensed, but also because his subjects are often very different from those in other books on GR like the one by Schutz. For one thing, he never uses the term "manifold", but talks about frame fields, which seem...

Hi. I am currently studying for my master's degree in physics. My credits for graduation are sufficient. But I am quite interested in GR. I have learned it by myself by studying two textbooks. In this new semester, I selected a course for GR. But in the first class, the professor did not give me...

Are there any experiments either already performed or even simply proposed that could be used to distinguish Einstein Cartan gravity from GR? My current understanding is that they are the same in vacuum, and only differ in matter. In matter the Einstein Cartan metric can have torsion, unlike...

I recently came across a book called advanced theoretical physics -nick lucid. chap6 covers tensors and chap 7&8 cover SR&GR. I have studied a bit of SR before but never GR. At this point in life I don't want to read huge books on the subject. this book covers relativity entirely in three...

Hi, there. I encounter the word "foliate" in GR textbooks but I have not seen it in other physics textbooks before. For example, it reads, we argue that a spherically symmetric spacetime can be foliated by two-spheres, from page 197 in spacetime and geometry by Carroll. By this sentence, I...

Hi, starting from this thread Principle of relativity for proper accelerating frame of reference I'm convincing myself of some misunderstanding about what a global inertial frame should actually be. In GR we take as definition of inertial frame (aka inertial coordinate system or inertial...

I have been reading the book Spacetime and Geometry by Sean Carroll, especially Ch. 2 Manifolds and Ch. 3 Curvature. I'm just wondering are there any lecture notes or books with lots of practice problems (with solutions or at least answers the better) that is suitable for physicist? To give an...

Assume a Schwarzschild black hole. Near the event horizon other than Hawking radiation the behavior of matter and energy are fairly accuratly described by general relativity. How close can one get to the center (the singularity based on GR) before one must switch to a quantum gravity theory...

Are you aware of the 3-article series of Wiesendanger's quantized extension of GR? This is open access: C Wiesendanger 2019 Class. Quantum Grav. 36 065015 and the two sequels linked to in the PDF. The question is if this work counts as a quantization of a reasonable extension or reformulation...

1. break down 430N [Up 35* L] into components 430 cos 35 = 352.2N [L] 430 sin 35 = 246.6N 2. ΣFx= 352.2N [L] ΣFy= 246.6N + 280N - 430N ΣFy = 86.6 3. Pythagorean theorem with the two will give you a magnitude of 362.7N Then using tan you can find the angle of [L 76 U] This method was...

Consider a celestial object distance d1 away from an observer, receding at v1=H0d1, Fig.a. And the same object at some time later, now at distance d2 and receding at higher speed v2=H0d2, Fig.b -- 1) where does the accelerating force come from? 2) the resulting universe-size vs time...

Note: My GR is very cursory and rusty. The probability that I say something bogus in stating my question is very high. Thanks for your help in advance! I have a dumb question. I'm only casually familiar with GR, and I have a hard time telling if quantities should be covariant or contravariant...

Hi, I'm a 15-year-old high school student and I was wondering what textbook you guys recommend for Special- and General Relativity. I'm familiar with the concept of the Metric Tensor and Christoffel Symbols, but I wanted a good textbook where I can really learn derive it all and gain a deeper...

I took differential geometry and introductory physics sequence in college, but not special relativity. How good are Leonard Susskind's lectures on YouTube for learning GR? Are there better sources to learn from?Thank you Edit: is learning SR a prerequisite for GR?

In my studies trying to get the Ricci tensor of 2° order i stuck in this expression: ##h_{\mu}^{\ \sigma},_{\lambda}h_{\sigma}^{\ \lambda},_{\nu}=h_{\mu \lambda},^{\sigma}h_{\sigma}^{\ \lambda},_{\nu}## So, to complete my calculations those quantities should be the same, but i don't understand...

The 2 Bowling Balls Ball(a) & Ball(b) (a) is in acceleration of 10m/s^2 (b) is in at fixed position in a gravitational field where g=10m/s^2 In both cases the observer is: - perpendicular to the vector of acceleration - distant enough to be in empty flat space Question : In an instantaneous...

Attached is a pic of the page in the book: My problem is with equation (11.34) specifically with the term ##\frac{6M^3}{L^2}y## I get ##L^4## instead of ##L^2##. Here are my calculations (I also checked it with maple's expand command)...