General relativity Definition and 999 Threads

Why do we use the equation ##\frac {1}{2}mv^2 = \frac {GmM}{r}## to derive potential velocity, and then put that in the Lorentz factor in order to derive gravitational time dilation? Shouldn't we be using the relativistic definition of kinetic energy -> ##mc^2(\gamma - 1)## to derive the...

We all heard about the "photo of black hole". My question is: did this image show any hints of physics beyond general relativity? I read once (not sure where) that the apparent size of black hole shadow is very sensitive to corrections to general relativity. Add some minor correction and the...

Does the Friedmann vacuum equation have a linear solution rather than an exponential one? Using natural units one can write Friedmann's equation for the vacuum as $$ \begin{eqnarray*} \left(\frac{\dot a}{a}\right)^2 &=& \frac{8\pi G}{3}\rho_{vac}\\\tag{1} &=& L^2 \left(\frac{\rho_0}{L^4}\right)...

Hello, I am an undergrad currently trying to understand General Relativity. I am reading Sean Carroll's Spacetime and Geometry and I understand the physics (to a certain degree) but I am having trouble understanding the notation used as well as the ideas for tensors, dual vectors and the...

Dear all, I have a question on Penrose diagrams. Consider a collapsing star that forms a black hole with a Schwarzschild radius normalized to 1. What happens in the Penrose diagram when additional matter falls in? I suspect the diagram then has to look like this : When the outer shell (second...

Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Kerr Spacetime Continue reading the Original Blog Post.

Since there is no privileged inertial frame, I would have expected the first particles in the universe to have no particular bias in their momenta. Relative to an observer I would expect the distribution to be uniform and unbounded. The mean momentum of the initial particles relative to an...

I am a student of physics at a local Junior College in Mendham NJ and am planning on transferring to a 4 year program at the University of Alabama in a year. Iam having a bit of a difficult time understanding general relativity. Why does a photon bend twice as much under a gravitational field...

Greg Bernhardt submitted a new blog post Fermi-Walker Transport in Schwarzschild Spacetime Continue reading the Original Blog Post.

Greg Bernhardt submitted a new blog post How to Study Fermi-Walker Transport in Minkowski Spacetime Continue reading the Original Blog Post.

Hello. I have some questions about general relativity that (I hope) will be permitted in this forum. Not long ago I discovered that there is more than one interpretation of GR. Now, I believe that the issue of interpretation is considered to be philosophy and therefore off topic. If that's...

According to the Big rip theory if Black holes tear apart after a very long time, then according to the theory of relativity an object that reaches the event horizon should see time passing infinitelty and by the time the object was swallowed wouldn't the black hole not exist anymore because of...

The Schwarzschild solution of the Einstein Equation of GR is said to be the only time-independent matter-free solution of that equation. In this usage, does “matter-free solution” mean without matter everywhere except at the singularity of the solution? I thought that the only solutions of the...

Hey my fellow physics-students/physicists. I'd like to ask if you guys could suggest me a textbook/s that sufficient for integrated course of "special" and "general relativity". More precisely, That contain about: Introduction about the birth of relativity and principle, and the transformation...

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?