General relativity Definition and 999 Threads

Hi everyone, I want to derive the Friedmann equations from Einstein Field Equations. However, I have a problem that stems from the energy-momentum tensor. I am also trying to keep track of ## c^2 ## terms. FRW Metric: $$ ds^2= -c^2dt^2 + a^2(t) \left( {\frac{dr^2}{1-kr^2} + r^2 d\theta^2 + r^2...

We know that Schwarzschild metric describes an asymptotically flat spacetime. This means that far away from the event horizon we can safely interpret the ##r## coordinate as distance from the center. But when close enough to the event horizon the curvature becomes significant and our common...

If we look Einstein equation ##G_{\mu\nu}=0##, which nontrivial aspects it can gives? One phenomenon is gravitational wave. I suppose that we are also free at initial conditions for this equation, thus we can begin with curved space time? What else?

Suppose that we want to compute the total time dilation for a clock located in an orbiting satellite relative to the clock in our cell phone on the ground. Consider two different approaches below. 1. Use special relativity and compute time contraction due to velocity. Use approximation of...

Reading the English translation of Einstein's seminal paper on GR. http://einsteinpapers.press.princeton.edu/vol6-trans/90?ajax This paragraph below on p78 doesn't make much sense to me. Could you provide a second English translation or even adding math notation. "Before Maxwell, the laws...

The geodesic general condition, i.e. for a non affine parameter, is that the directional covariant derivative is an operator which scales the tangent vector: $$\zeta^{\mu}\nabla_{\mu}\zeta_{\nu}=\eta(\alpha)\zeta_{\nu}$$ I have three related questions. When $$\alpha$$ is an affine parameter...

Hello, I wanted to know how Einstein's General Relativity and its equations simplify to Newton's Universal Law. Einstein's equation is obviously a much more generalized version of Newton's law and gives much more accurate predictions that Newton's laws even if we don't think of Newton's gravity...

Hey there, I have two questions - the first is about an approximation of a central gravitational force on a particle (of small mass) based on special relativity, and the second is about the legitimacy of a Lagrangian I'm using to calculate the motion of a particle in the Schwarzschild metric...

Homework Statement A clock moving at v = (3/5)c reads 12:00 as it passes us in our frame of reference, how far away will it be (in light hours) when it reads 1:00. Homework Equations I denote a prime to mean the reference frame of the clock at rest. I use regular lettering to denote 'our'...

I was trying to solve this excercise: Now I was able to find the eq. of geodetics (or directly by Christoffel formulas calculation or by the Lagrangian for a point particle). And I verified that such space constant coordinate point is a geodetic. Now, for the second point I...

Hi,I'd like to build a simulation (realtime) of space ships near a black hole (neutral, still or rotating possibly). Key features would be: 1) the ships are test particles that do not affect the metric a) possibly test rigid-bodies with GR consistent rotational DOF. 2) the ships can fire...

When does GR apply in gravitational fields as opposed to Newtonian gravitation? Another words, what would be the strength of the graviatational field before we abandon Newtonian gravity and start implementing GR? 10 g's, 20 g's?

I just want to share my paper I recently wrote. I am trying to submit for publication: [Reference to unpublished paper deleted]

By reading on the internet I ve found various websites talking about the relation between gravitation and electromagnetism, and in particular, under: - "Small" Gravitational fields -"small" changes in energy with respect to time, The linearized enstein' s field equation becomes pretty much...

Hello all. I am self teaching physics, and after completing Classical Mechanics (Special Relativity included), Classical EM and an introductory course to QM, I would like to take a very introductory look to General Relativity. With this purpose in mind, I have chosen 2 books, and I would like...

Hello I am little bit confused about lagrange approximation to geodesic equation: So we have lagrange equal to L=gμνd/dxμd/dxν And we have Euler-Lagrange equation:∂L/∂xμ-d/dt ∂/∂x(dot)μ=0 And x(dot)μ=dxμ/dτ. How do I find the value of x(dot)μ?

Hello, If anyone could help me with the prerequitisetes for an undergraduate General Relativity and Cosmology course I will enroll into, It will be much appreciated. The syllabus is the following(sorry for the rough translation): -Review of Special Relativity -Spacetime in GR -Geodesics...

Hello everyone, There is something that has been bugging me for a long time about the meaning of Lorentz Transformations when looked at in the context of tensor analysis. I will try to be as clear as possible while at the same time remaining faithful to the train of thought that brought me...

There's lots of other questions on the forum about 2 black holes, but I think this is different - and I can't get my head around which outcome is consistent with GR. Black holes here are simplistic - non-rotating and let's assume with a tiny accretion disk; just enough grains of matter to allow...

Bill_K submitted a new PF Insights post https://www.physicsforums.com/insights/precession-special-general-relativity/ https://www.physicsforums.com/insights/precession-special-general-relativity/

CPT symmetry and antimatter gravity in general relativity M. Villata Published 28 March 2011 • Europhysics Letters Association EPL (Europhysics Letters), Volume 94, Number 2 Abstract The gravitational behavior of antimatter is still unknown. While we may be confident that antimatter is...

In the paper Strong field limit of black hole gravitational lensing, the amplification of images in the Schwartzschild metric was given by $$ \frac{1}{\beta}\sqrt{\frac{2\,D_{LS}}{D_{OL}D_{OS}}} $$However the authors did not derive this expression or explain its origin. Does anyone know how to...

Can one shed light on the velocity of the photon through the fourth dimension x4 using limits? To begin with, please study the mathematics from Brian Greene’s book An Elegant Universe. The upshot is that the faster an object moves through space, the slower it moves through the fourth...

Hello, Is the book General Relativity by Hobson, Lasenby and Efstathiou good in the sense that is intuitive on the mathematics AND physics that it presents? Please vote and if you could also comment your opinion it would be much appreciated. Thanks!

I would like to study more about the notion of time in modern physics. In particular, I would like to understand better the following question: how does one measure the time in the early universe? To measure time one needs to have clocks. A natural choice to be used as clocks would be particles...

I'm trying to prepare to read The Large Scale Structure Of Space-time by Hawking and Ellis. I've been reading a General Topology textbook since the authors say "While we expect that most of our readers will have some acquaintance with General Relativity, we have endeavored to write this book so...

I am hoping someone can clarify some confusion I have. It is my understanding that there is no such thing as absolute velocity or acceleration in GR. If one observer is moving near the speed of light and the other is stationary each observer will see the other as in motion. But if they each...

What 20 index combinations yield Riemann tensor components (that are not identically zero) from which the rest of the tensor components can be determined?

Hello, I was wondering if anyone knows about the the book "The Geometry of Spacetime: An Introduction to Special and General Relativity" by Callahan and what their opinions are. Thanks!

Hello, I would like to know if anybody here has used the book "Differential Forms and the Geometry of General Relativity" by Tevian Dray and how they found it. Thanks!

Where can I find a derivation of the vacuum solution for GR directly from the Riemann tensor of zero trace, i.e., Weyl tensor, instead of the more traditional Schwarzschild derivation?

From the weak EP, inertial mass is equivalent to the gravitational mass. The weak EP implies the universality of gravitation. Some implications of the EP are: 1) Gravity is inescapable - there is no such thing as gravitationally neutral object with respect to which we can measure the...

Where can I find a free digital copy of The Large Scale Structure of Space-time by Hawking and Ellis?

I'm fairly new to differential geometry (learning with a view to understanding general relativity at a deeper level) and hoping I can clear up some questions I have about coordinate charts on manifolds. Is the reason why one can't construct global coordinate charts on manifolds in general...

I've recently been studying a bit of differential geometry in the hope of gaining a deeper understanding of the mathematics of general relativity (GR). I have come across the notion of a topology and whilst I understand the mathematical definition (in terms of endowing a set of points with the...

Hi. There were theoretical (find transformations under which Maxwell's equations remain invariant) and experimental (speed of light is constant, Michelson-Morley) indications that made the development of SR inevitable. But what about GR? Was there a "need" for this theory or was Einstein just...

Hello everyone, I've come across a problem that i can't solve but which i find really interesting. I'm not here to ask where the big bang was because I've already read enough about that is was a singularity, so you could say that is was everywhere. But here my problem comes in, if the big bang...

What is the metric for the spacetime around an infinitely thin, infinitely long, uniform rod? Could it be written in the form ds2 = A(r)dt2 + B(r)dr2 + C(r)dh2 + r2dθ2 where h is the coordinate along the rod and r is the radial coordinate, or would it be something more complicated?

With length contraction being ever increased while approaching the mass of a black hole singularity, how does one measure the distance to the virtual infinite contracting frames of reference of time and space /distance of the singularity? Related question : How can one measure the size of a...

Hello again, I would like to know what your opinions about this book. As I have figured out, there are a lot of great GR books out there, but this very rarely gets any mention in forums like this. Why is this? Its got pretty good reviews at amazon and goodreads. Thanks in advance!

I have heard/read that Carroll's Spacetime and Geometry: An Introduction to General Relativity is one of the best books on General Relativity but its price is insanely high! Does anybody know any place which sells it at a lower price than, say, Amazon? If not, what are other books that cover...

What happens when charged particles fall into a black hole? Say like N electrons fall in, giving the black hole a net charge of -N. Since light cannot escape the event horizon, I imagine electric fields cannot either, since they are mediated by photons. So is that charge effectively lost until...

Hi, I would like say that in this link ( ) and starting from 56.28 Suskind tries to find the energy tensor equation using \phi, afterwards he finds a equation similar to wave equation in terms of \phi. My question is: For what does \phi stand ? I could not capture the meaning of \phi. Could...

Goodmorning everyone, is there any implies to use in general relativity a metric whose coefficients are harmonic functions? For example in (1+1)-dimensions, is there any implies for using a metric ds2=E(du2+dv2) with E a harmonic function? In (1+1)-dimensions is well-know that the Einstein...

I am reading general and special relativity from a book and I am stuck with these lines please can someone provide its detailed explanation "Einstein demanded that the special principle of relativity should be valid also for Maxwell’s electromagnetic theory. This was obtained by replacing the...

It is known that equivalence principle is good for understaning of general relativity (GR). This means comparison of the elevator and falling in homogenic gravitational field. But, I here somewhere something like "in the higher lever of GR, let us forget on principle of equivalence". How it is...

I have read several times that general relativity has some problems with quantum mechanics and they are not compatible. However, special relativity can be introduced in quantum mechanics mainly by Dirac equations (so I am pretty sure that the problem of passing from a frame where the parameter...

HI, can anyone suggest a good book on general relativity with fairly good mathematics for beginner for self study?

The Galilean equivalence principle (or weak equivalence principle) is the statement of the universality of free-fall under gravity. For example, according to Wikipedia, it can be stated as follows My question regards the limitation of the principle to point masses. Does universality of...

If I spin around in an open field at night and look up to the stars they appear to be moving relative to me. Additionally, they are very far away and trace out a giant arc length in a very short time (S=rθ). With respect to me, these stars are moving faster than light. Is this a problem? Has...