General relativity Definition and 999 Threads

I have a question about the concept of length contraction. The black line from (0, 0) to (1, 0) represents a meter stick in my stationary frame, call it frame A. The blue axes represent my coordinate system with coordinates x and t. The green axes represent the coordinate system of a moving...

Although there are tons of experimental tests/confirmations for General Relativity, I noticed that most of them are made on/from Earth, or very close to Earth, so in this thread I'll suggest 2 extensions of past experiments: 1. GSM GPS satellite (preferably with an unmodified atomic clock) far...

Hello, I'm studying General Relativity using Ray D'Inverno's book. [Moderator's note: link deleted due to possible copyright issues.] . I don't understand what the author writes in paragraph 14.3 ("Static solutions") where he demonstrates that for a static spacetime there are no cross-terms...

Section 5 (pg. 29) of the Michel Janssen's paper EINSTEIN’S QUEST FOR GENERAL RELATIVITY, 1907–1920(*) says: 1. From the above I understand that the application of general relativity to an infinite universe was considered problematic. 2. On the other hand, I understand that it is currently...

A Kerr Black Hole (BH) is a spinning BH. There is an Event Horizon (EH) which is $$r_H^\pm = \frac{r_S \pm \sqrt{r_S^2 -4a^2}}{2}$$ where ##a=\frac{J}{Mc}## and ##r_S## is the Schwarzschild radius. My question is, suppose I'm in a spacecraft, not in orbit, but stationary at a distance ##r##. I...

A technical subject, well above my level it seems (I'm still learning about quantum physics and special relativity), but one about which I absolutely must get some clear ideas as soon as possible. From what I 'understand', Noether's second theorem applies to infinite-dimensional symmetry...

I'll set out by saying that I have no real formal training in physics or maths. However, I have been keen to try to understand what exactly convinced Einstein that spacetime must be curved. As I understand it, the bending of star light was already explained by Newtonian physics, although of...

i have just started on relativity, so be simple. you are going to travel 1 lightyear at half the speed of light. therefore, it would take 2 years to travel 1 lightyear. on Earth, you would see me going half the speed of light, so it should take two years as well? i calculated gamma as being...

I am looking at some of the threads on the twin paradox, and getting even more confused. I have been trying to run through the details of what each twin is seeing, and was wondering if I could get some help. I am just trying to imagine how each twin is “seeing” the other twin at each step as the...

I very often see in movies and works of fiction that scientists explain that with a black hole you can travel in time and how the characters use black holes to travel in time, more precisely to the past Do scientists really believe that time travel through black holes is likely? If so, why?

(I) Using the relevant equation I find this to be ## \frac{e^{x}}{2} ##. (II) Using the relation for the Ricci tensor, I find that the only non-zero components are...

The following is more of an interesting example and observation than a question that I am presenting for public comment. It's somewhat related to a recently thread, which was closed for moderation, but I think it's different enough not to fall under the ban of reposting threads that have been...

I encountered a problem in reading Phys.Lett.B Vol.755, 367-370 (2016). I cannot derive Eq.(7), the following snapshot is the paper and my oen derivation, I cannot repeat Eq.(7) in the paper. ##g^{\mu\nu}## is diagonal metric tensor and##g^{\mu\mu}## is the function of ##\mu## only...

Studying and tinkering with some solutions, I've come to some realizations and questions regarding the regularization of coordinate singularities, so I'd like to see if my conclusions are good, and I guess I have some questions as well. There are two questions/conclusions, but since they...

Hello everyone, I am a couple of months away of starting my PhD in Numerical Relativity and I am seeking recommendations for references to get a batter understanding on the mathematical foundations of GR and topics of Numerical Relativity. So far I have had an undergraduate introductory course...

GR has very limited situations in which a total mass-energy can be defined. The Komar mass, for example, requires the presence of a timelike killing vector field and an asymptotically flat spacetime. Basically, if the metric change with time or it's spacelike curvature does not flatten out...

I bought a copy of Adler's new book on relativity. Is there a misprint on page 16 regarding the Lorentz metric = diag (-1,-1,-1,-1) or am I missing something? The text itself after the equation suggests it is the same metric as on the earlier page so that index placement, two lower indices vs...

What is the metric for a bag-of-gold spacetime?

Black holes are everywhere in astrophysics. There are numerous discussion about how black holes look like, what happens to gas falling into black holes, how light bends around black holes, whether there is loss of information when mass or energy falls in, etc. There is thought to be a black hole...

I have the following question to solve:Use the metric:$$ds^2 = -dt^2 +dx^2 +2a^2(t)dxdy + dy^2 +dz^2$$ Test bodies are arranged in a circle on the metric at rest at ##t=0##. The circle define as $$x^2 +y^2 \leq R^2$$ The bodies start to move on geodesic when we have $$a(0)=0$$ a. we have to...

Are there any metrics for intra-universe wormholes?

I found this interesting discussion here in Physics Forums (https://www.physicsforums.com/threads/are-all-symmetries-in-physics-just-approximations.1005038/) where the topic of all symmetries being approximate is discussed Is there any model (for instance, some type of spacetime metric or...

In the book general relativity by Hobson the gravitational wave of a binary merger is computed in the frame of the binary merger as well as the TT-gauge. I considered what components of the Riemann tensor along the x-axis in both gauges. The equation for the metric in the source and TT-gauge are...

I am studying metrics that exhibit CTCs. I was looking at a few different metrics... Tipler's solution Godel metric Kerr metric For starters to compare them, I am trying to convert said metrics into cylindrical coordinates. Thanks in advance for any help😃

Hi, I am looking to study general relativity at my own steam (currently finishing 1st year physics at Warwick) during the summer. What textbook(s) would you recommend? I've heard good things about A. Zee's 'Einstein Gravity in a Nutshell'- is that worth it, and would it be suitable for someone...

Is it generally the case even with light like paths that ##\dot t>0##?

I know nothing about physics, to be clear. My friend was saying due to general relativity, the faster you move through space, the slower you move through time. Objects with a heavy mass (like a blackhole) can distort the fabric of space time and being near its gravitational pull means that you...

I was reading a discussion where some physicists participated* where the topic of Lorentz invariance violations occurring in cosmology is mentioned. There, they mention that we can imagine a Lorentz-violating solution to the cosmological equations. What do they mean by that? Can anyone specify...

A minimally coupled scalar field can model a cosmological fluid model where And where the equation of state can be the standard ## \omega = \frac {p} {\rho}## I can see how this does a fine job modeling matter, because as the scale factor increases, the density will go as ##\frac {1} {a^3}##...

Let's say we have some observer in some curved spacetime, and we have another observer moving relative to them with some velocity ##v## that is a significant fraction of ##c##. How would coordinates in this curved spacetime change between the two reference frames? For example, imagine a...

I started by expanding ##dx## and ##dt## using chain rule: $$dt = \frac{dt}{dX}dX+\frac{dt}{dT}dT$$ $$dx = \frac{dx}{dX}dX+\frac{dx}{dT}dT$$ and then expressing ##ds^2## as such: $$ds^2 =...

• CERN talk : indico.cern.ch/event/1153372/contributions/5200955/ • Presentation materials : bit.ly/MAGIC23AMayer • CERN MAGIC23 : indico.cern.ch/event/1153372/ Talk Description (Abstract) We present empirical evidence from the Sloan Digital Sky Survey (SDSS), including...

I have some questions regarding the expected exchange particles for gravitation. From my understanding the following was valid: We can linearize the equations of GTR for weak fields "Quantum mechanics" (Schrödinger, Dirac equations) are linear Those linear equations allow eigenstates and...

Hi, I am reading through my lecture notes - I haven't formally covered killing vectors but it was introduced briefly in lectures. Reading through the notes has highlighted something I am not sure about when it comes to co-ordinate transformations. Q1.Can someone explain how to go from...

In the context of the Theory of Relativity are there any spacetimes or metrics with a complete absence of symmetries? I mean, consider a type of space or metric where no symmetries would hold (at least not exactly, but approximately). A space or metric where the Poincaré invariance (including...

In Dirac's "General Theory of Relativity", at the end of Ch. 25 (p. 47), right after deriving the full Einstein equation ##R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R = -8\pi\rho v^\mu v^\nu = -8\pi T^{\mu\nu}##, he makes a reference to the conservation of mass (Eq. 25.3): $$0 = (\rho v^\mu)_{:\mu} =...

This time with General Relativity: https://www.amazon.com/dp/1541601777/?tag=pfamazon01-20 I got a copy as soon as I noticed it. And it is good - as all his books are. Notice - number one best seller. Lenny deserves a medal. There is a genuine thirst for science beyond banal...

Hello, everyone I am now working on this project quite a while now and I just wanted to share it with this forum, which I was a member for a long time. I am working on a python application about GR and I believe I managed to create a very user-friendly layout. It's called GTRPy, and it allows...

Here is the video: [link deleted by moderators] His basic idea is to take the spacetime interval and add a 5th term for the 5th dimension he is describing so it looks like: $$\Delta S^2 = c^2\Delta t^2 + c^2\Delta w^2 - \Delta x^2 - \Delta y^2 - \Delta z^2 $$ where w is the difference in time...

When arriving at the standard model of cosmology, i.e. the exapnding universe, we assume based on experirmental data that the cosmos is homogenous on large enough scales. But when we go back in time, when the galaxies are beginning to form, we note that because of the growth of density...

Modeling the time evolution of the sun and earth orbiting each other using ##F = \frac{GMm}{r^2}## is straightforward. However, it appears that modeling the time evolution of the same 2 body system using general relativity seems to be a hard/intractable problem? There was in depth discussion by...

Einstein showed (via general relativity) that spacetime is curved by mass, mass moves in relation to this curvature, and that gravitation arises as secondary effect. Why then are we looking for quantum gravity as some sort of mass<->mass interaction? Aren't the fundamental interactions better...

I was reading this paper (*Green's functions for gravitational waves in FRW spacetimes:* [https://arxiv.org/abs/gr-qc/9309025](https://arxiv.org/abs/gr-qc/9309025)) and I had a specific question about one statement in the paper that I would like to ask: At page 6, the author says that...

About a month or two ago I started doing simulations of light physics around black holes and yesterday I got a fast Christoffel symbols function for the Schwarzschild metric in cartesian coordinates, but now the photon ring appears flipped. I feel as though it is wrong. But as I am still pretty...

For some time I was wondering, what would happen if the Sun just disappeared like someone hit the delete button in Universal Sandbox. Specifically, what kind of gravitational waves will be produced in the wake of such an event? Would the law of conservation of Mass-Energy be miraculously...

It's possible that this may be a better fit for the Differential Geometry forum (in which case, please do let me know). However, I'm curious to know whether anyone is aware of any standard naming convention for the two principal invariants of the Weyl tensor. For the Riemann tensor, the names of...

I'm wondering is I'm missing something, or this should be " a non-zero component"?

Does anyone know of a comprehensive list of solutions to GR, their developmental history, and the viability for serving as a practical model for the observable universe?

Once having converted the FLRW metric from comoving coordinates ##ds^2=-dt^2+a^2(t)(dr^2+r^2d\phi^2)## to "conformal" coordinates ##ds^2=a^2(n)(-dn^2+dr^2+r^2d\phi^2)##, is there a way to facilitate solving for general geodesics that would otherwise be difficult, such as cases with motion in...

How do I calculate the unit normal vector for any metric tensor?