General relativity Definition and 999 Threads

This week I am at "General Relativity as a Challenge for Physics Education" 690. WE-Heraeus-Seminar https://www.we-heraeus-stiftung.de/veranstaltungen/seminare/2019/general-relativity-as-a-challenge-for-physics-education/ (...

How do you know what fields can be coupled with the gravitational field? Is there a general procedure for knowing it or we have to try out and see whether it makes sense or not?

A while back I posted a black hole horizon puzzle. This is another puzzle in the same general spirit. It is based on the scenario described in this old PF thread: https://www.physicsforums.com/threads/a-flaw-of-general-relativity.115418/ Needless to say, as was the case with my previous...

I am working on a research project where I intend to describe what the Penrose process would like in a sonic black hole. I have found what a rotating (Kerr) black hole looks like in the sonic analog: https://arxiv.org/pdf/1802.08306.pdf I have also found that the analog of massless particles...

Does General Relativity allow for transformations which are not isometries of the metric?

I am reading Carroll’s Spacetime and Geometry, and I have seen the word “coupled” used multiple times in seemingly different ways. I have gotten the sense that it means some sort of interaction between particles, but Carroll refers to coupling between matter fields and the curvature of...

Hi, There is a point that, in my opinion, is not quite emphasized in the context of general relativity. It is the notion of spacetime coordinate systems that from the very foundation of general relativity are assumed to be all on the same footing. Nevertheless I believe each of them has to be...

Hi, I'm trying to deduce orbit velocity of a particle with mass from Schwarzschild metric. I know for Newtonian gravity it is: $$v^2=GM\left(\frac{2}{r}-\frac{1}{a}\right)$$ The so called vis-viva equation. Where ##a## is the length of the semi-major axis of the orbit. For Schwarzschild metric...

Hello. The book "General Relativity, Astrophysics, and Cosmology", by Raychaudhuri, et al., looks like a good compact exposition of GR, astrophysics and cosmology, which is exactly the kind of book I'm looking for. What do you think of this book? Thank you in advance.

Greetings: I can understand that an object's trajectory curves about a greater mass (e. g., satellite in Earth's orbit). The spacetime is curved via the great mass and the moving object simply follows the curvature. My problem is this: Why does a stationary object at a short distance from...

Is it possible to calculate with precision the orbits of the Earth, Moon and Sun with general relativity instead of Newtonian Physics? How would this work? Would the software have to record past positions of each body and have the Earth be attracted to the old sun's position 8 minutes ago...

After making a couple of comments on this StackExchange question, and pointing yet again to this article, a thought occurred to me. I have been working on an Automatic Differentiation based ODE solver and equation analyzer, mentioned in this thread. Why not use it to solve equation (7) in the...

I would like to know if there are any Physics Instructors or Professors who may believe that Queuing Theory as well as Relativity Theory may be relevant to CPE where communications platforms are moving at relativistic velocities with respect to (wrt) each other?

So, I am confused about the following.I learned in high school and in my first year of university that there is something called time dilation that observers observe that time is slower for objects that are moving faster. As in if there were two initially synchronized clocks that you could...

Are there a lot of theoretical research jobs in general relativity or would that be too hard to find?

Maybe I'm just being stupid, missing something simple ? How do you get from the top two equations to the second equation? Many thanks

Hi, It is usually claimed that a person in an accelerating elevator with an acceleration equals to the gravity of the earth; this person cannot make any experiment that makes him know whether he is in the elevator or on the surface of earth. However, if this person project two light beams...

Hi, Do we obtain the same escape velocity equation: Ve = sqrt(2GM/r) using both Newtonian and Relativistic approach?

I am collecting ways to visualize the curvature of spacetime -- and movement of objects affected by gravity -- as per Einstein's GR. Alternatives to the bowling ball / trampoline image so often used in the popular press. Images that show the similarities / differences between Newton & Einstein...

Background: I'm about to graduate with a mathematics degree(in the US), hence I have exposure to multivariable calculus, real analysis, abstract algebra, complex variables etc (no differential geometry however). I have also taken a class on QM(using Griffiths) and I saw some SR during a Modern...

In my physics education, I shied away from heavily theoretical stuff like General Relativity. I took the required sequence in Quantum Mechanics but having never used it on the job, much of that knowledge has faded too. I started a course in Quantum Field Theory but dropped it. I had friends...

Is there a sensible way of defining a displacement vector in a general manifold? That is, the displacement vector being the difference between position vector at two different points... the problem is that these two different points have, in general, different tangent vector spaces. Never the...

Hi, I'm wondering if it is possible to measure radii of stars using general relativity, given its explanation of gravity as curvature of space. Thank you

I am still learning general relativity (GR). I know we can find the path of a test particle by solving geodesic equations. I am wondering if it is possible to derive/convert metric tensor to gravity, under weak approximation, and vice versa. Thanks!

This is an inquiry about some of the details of the bending of the trajectory if a photon by curved space-time (S-T) from the perspective of general relativity (GR). The environment in this scenario contains a black hole at its center, a photon passing by the black hole a km above the event...

If someone wanted to pursue a career in gravitational wave physics, and work at places like LIGO, studying astrophysical objects such as black holes and neutron stars, etc. What are some key courses/skills that person should take/learn as an undergraduate, and graduate student?

I have little exposure to mathematics beyond high school algebra and physics, but I have become increasingly interested in physics, particularly its most towering achievements of modern times : Quantum Physics, as well as A. Einstein’s Special and General Relativity, the latter of a...

After I read Martin_K's post of 4:14 Oct. 30 on the frozen image of an object just before it fell through a black hole's event horizon, the next few minutes I was jumped by a handful of related ideas. First, the frozen image scenario is illustrative because when photons are frozen in place...

Hi, the trace of the extrinsic tensor K(Myu,Nu) in Alcubierre metric, relative to the foliation normal vector is non zero on the front x=rs+R and rear x=rs-R "walls". This is the normal volume component Tr =k(1,1)+k(2,2)+k(3,3) and should affect the Ricci tensor in Lorentzian/Minkowsky 4D. How...

What is currently the common opinion on Chronology Protection manifested by Hawking almost 30 years ago? There does not seem to be any fully accepted no-go result for Thornian time machines. Energy conditions can be violated in QFT, semi-classical results suffer from counter-examples, Novikov's...

Is the increase in mass/density of an object in motion purely relativistic? What I mean is if you were in a spaceship approaching the speed of light would you be able to measure a change in your mass/density or would the change only be observable to someone at rest. I'm aware of the Lorentz...

Hi. I want to learn - amateurishly - Quantum Mechanics, and General Relativity, but my experience with Physics is very small. I want to ask, what should I learn - what books should I read - before I start to learn those theories? Sorry for my english.

Any one please refer some text for general theory of relativity, Also share some link of PDF about GTR

Hello, I was wondering if somebody could help me by suggesting a concrete topic in GR for my master's dissertation. My background is from Mathematics, but I have followed first year masters program courses in Theoretical Physics, including one on General Relativity based on Schutz's book...

As far as I know, a object will experience time slower when its speed is close to the speed of light. But photons themselves moves at the speed of light, does that mean that they experience no time?

I will be proceeding onto my masters degree in theoretical physics in about two months time. My goal is to learn as much as I can about quantum and statistical physics, as this is the field in which I would like to do my PhD. In my second semester, I have the chance to either study the...

Hi, I have the following problem: Given the 5-D generalization of the Schwarszschild solution with line element: ds^2=-\Bigg(1-\frac{r^2_+}{r^2}\Bigg)dt^2+\Bigg(1-\frac{r^2_+}{r^2}\Bigg)^{-1}dr^2+r^2[d\chi^2+\sin^2(\chi)(d\theta^2+\sin^2(\theta)d\phi^2)] where ##r_+## is a positive constant...

Hi, I'm the given the following line element: ds^2=\Big(1-\frac{2m}{r}\large)d\tau ^2+\Big(1-\frac{2m}{r}\large)^{-1}dr^2+r^2(d\theta ^2+\sin ^2 (\theta)d\phi ^2) And I'm asked to calculate the null geodesics. I know that in order to do that I have to solve the Euler-Lagrange equations. For...

I am making this thread to discuss interesting open questions in Gravity and Cosmology with people working in these or even relevant area. Anyone who is working in these (and relevant) areas, please identify yourself here and we will begin and hopefully people will catch on and contribute.

I am doing a problem from Schutz, Introduction to general relativity.The question asks you to find a coordinate transformation to a local inertial frame from a weak field Newtonian metric tensor ##(ds^2=-(1+2\phi)dt^2+(1-2\phi)(dx^2+dy^2+dz^2))##. I looked at the solution from a manual and it...

It had previously been verified within our own galaxy. http://uopnews.port.ac.uk/2018/06/22/einstein-proved-right-in-another-galaxy/

Greg Bernhardt submitted a new PF Insights post How to Better Define Information in Physics Continue reading the Original PF Insights Post.

I have a question. I know that events don't happen simultaneously but rather they are ordered chronologically by time, but why? What is time and how does it stretch events and why does it have the rhythm/flow that it currently has?

Homework Statement This is Problem 2 from Chapter 1, Section V of A. Zee's Einstein Gravity in a Nutshell. Zee asks us to imagine a colony of "eskimo mites" that live at the north pole. The geometers of the colony have measured the following metric of their world to second order (with the...

Homework Statement Hi everyone! Just wondering if there's a way to prove the symmetry property of the Riemann curvature tensor $$ R_{abcd} = R_{cdab}$$ without using the anti-symmetry property $$ R_{abcd} = -R_{bacd} = -R_{abdc} $$? I'm only able to prove it with the anti-symmetry property and...

If dark matter is a supersolid that fills 'empty' space and is displaced by visible matter, then is this the same notion as the spacetime fabric having mass and being curved by visible matter?

I've been reading up on Killing vectors, and have got on to the topics of homogeneous, isotropic and maximally symmetric space-times. I've read that for an isotropic spacetime, one can construct a set of Killing vector fields ##K^{(i)}##, such that, at some point ##p\in M## (where ##M## is the...

So the other day I saw a YouTube video on how gravity works according to general relativity. From what I understand, objects bend space_time with their mass and create a shape which is close to a cone. Since objects only move forward in time through a straight line, the bent space_time makes...

Hello everyone, I'll go straight to the question. The gravitational time dilation is equal to tearth = tspace*sqrt(1 - rs/r), with rs = 2GM/c2. However, the formula for speed of light in gravitational field is equal to v = c(1 - rs/r). My intuition tells me that these two formulas must be the...

Greg Bernhardt submitted a new PF Insights post Solving Einstein's Field Equations in Maxima Continue reading the Original PF Insights Post.