General relativity Definition and 999 Threads

I have seen written out in various places (including this forum) the effective potential function that comes from the solutions to the Schwarszschild Geodesic. But I haven't been able to find the effective potential functions for other solutions to Einstein's field equations. Are there...

http://en.wikipedia.org/wiki/Kaluza–Klein_theory ##http://link.springer.com/article/10.1007/BF01390677 (original german paper, Ich kan nicht Deutsche) http://www.scientificexploration.org/journal/jse_21_3_beichler.pdf (this author makes some interesting arguments) Also, a lot (if not all...

Homework Statement (a) Show that the equations satisfy FRW equations. (b) Show the metric when ##\eta## is taken as time Homework EquationsThe Attempt at a Solution [/B] The FRW equation is: 3 \left( \frac{\dot a}{a} \right)^2 = 8\pi G \rho Using ##\frac{da}{dt} = \frac{da}{d\eta}...

What do they mean by 'Contract ##\mu## with ##\alpha##'? I thought only top-bottom indices that are the same can contract? For example ##A_\mu g^{\mu v} = A^v##.

I have been reading section 3.1 of Wald's GR book in which he introduces the notion of a covariant derivative. As I understand, this is introduced as the (partial) derivative operators \partial_{a} are dependent on the coordinate system one chooses and thus not naturally associated with the...

What do they mean by contracting ##\mu## with ##\alpha## ?

Homework Statement (a) Show acceleration is perpendicular to velocity (b)Show the following relations (c) Show the continuity equation (d) Show if P = 0 geodesics obey: Homework EquationsThe Attempt at a SolutionPart (a) U_{\mu}A^{\mu} = U_{\mu}U^v \left[ \partial_v U^{\mu} +...

Homework Statement [/B] (a) Find the proper distance (b) Find the proper area (c) Find the proper volume (d) Find the four-volume Homework EquationsThe Attempt at a Solution Part (a) Letting ##d\theta = dt = d\phi = 0##: \Delta s = \int_0^R \left( 1-Ar^2 \right) dr = R \left(1 -...

Starting with the geodesic equation with non-relativistic approximation: \frac{d^2 x^{\mu}}{d \tau^2} + \Gamma_{00}^{\mu} \left( \frac{dx^0}{d\tau} \right)^2 = 0 I know that ## \Gamma_{\alpha \beta}^{\mu} = \frac{\partial x^{\mu}}{\partial y^{\lambda}} \frac{\partial^2 y^{\lambda}}{\partial...

Homework Statement Find the deflection of light given this metric, along null geodesics. Homework EquationsThe Attempt at a Solution [/B] Conserved quantities are: e \equiv -\zeta \cdot u = \left( 1 - \frac{2GM}{c^2r} \right) c \frac{dt}{d\lambda} l \equiv \eta \cdot u = r^2 \left( 1 -...

Homework Statement (a) Find the proper time in the rest frame of particle (b) Find the proper time in the laboratory frame (c) Find the proper time in a photon that travels from A to B in time P Homework EquationsThe Attempt at a Solution Part(a) [/B] The metric is given by: ds^2 =...

I was reading my lecturer's notes on GR where I came across the geodesic equation for four-velocity. There is a line which read: Summing them up, \partial_i g_{aj} u^i u^j - \frac{1}{2} \partial_a g_{ij} u^i u^j = \frac{1}{2} u^i u^j \partial_a g_{ij} I'm trying to understand how LHS = RHS...

We know that when a rigid frame, say a rocket undergoes constant proper acceleration, its worldline is hyperbolic. The equation is given by: x^2 - c^2t^2 = \left( \frac{c^2}{a_0} \right)^2 Suppose P is such a worldline and worldine can also be written as: I understand how these are...

If $$e^1$$ is a form like the ones in tetrad formalism (vielbeins). If we have $$e^1 . e^1$$ can we treat those as basis like $$i.i=1$$?

Homework Statement (a) Find matrix element ##M_{ij}## (b) Show that ##x^j## is an eigenvector of ##M_{ij}## (c) Show any vector orthogonal to ##x^j## is also an eigenvector of ##M_{ij}## Homework EquationsThe Attempt at a Solution Part(a) [/B] \frac{\partial^2 \Phi}{\partial x^i x^j} =...

I have studied most of the concepts of Newtonian mechanics and understood the calculations and derivations involving the concerned formulae. I have a basic knowledge of calculus (differentiation of products along with differentiation of trigonometric, logarithmic, exponential and implicit...

I am trying to derive the gravitational red shift effect but I think I am going about it all wrong. Specifically, I want to derive the change in frequency/ wavelength when a photon moves away from the surface of a star mass M and radius R. So I tried to use relativistic mass of the photon and I...

I read in a magazine (namely Scientific American) that the Standard Model successfully combines Quantum Mechanics with General Relativity, but I also remember reading in The Elegant Universe that the Standard Model fails to do so. What's true and what's not?

Hi all, I'm fairly new to GR, and I'm also somewhat new to tensors as well. I'm looking for some detailed explanation of a tensor, as I want to begin studying GR mathematically. I watched a video that was posted on PF not too long ago that was pretty good. I'm having trouble remembering who it...

Hello, Everybody! I'm new to the board, and am happy to have found you! I have six questions I can't seem to find the answers to, either in books or online -- yet I know the answers are out there! I'll post each question in a separate thread, and hope that someone who knows far more than I do...

I understand that all physical laws essentially codify mathematically observed behavior. Newton codified Kepler and Brahe data, for example. Quantum Mechanics codifies observed particle behavior at relatively low speeds, etc. But Einstein had no empirical data to work from… So, I do not...

Homework Statement Suppose everything is moving slowly, How can we find the metric tensor in GR in terms of the mass contained. Homework Equations I understand in case of everything moving slowly only below equation is relevant - R00 - ½g00R = 8πGT00 = 8πGmc2 The Attempt at a Solution None.

In considering special relativity as a limiting case of the general theory (without matter or curvature) the question arose as to whether the pseudo-riemann nature of the SR metric is actually an independant (essentially experimentally determined) assumption/property or derivable from the...

Is it true than general relativity can be deduced from a maximum mass density for matter?

I am currently learning general relativity and I kind of understand what the symbols in einstein field equationd represent. But I need example like those that involves actual numerical values. I have been trying to search for it online but I cant. So does anyone mind showing me how you apply...

How can it be deduced general relativity from Planck length?

Let's assume the Earth was perfect sphere with radios of 6,750,000 meters. There are 3 clocks , one will not move one will move west in velocity V and the other will move east in the same velocity. The Earth is still rotating. So one clock is going with the Earth rotation and the outher is going...

Hello all, I have a quick question regarding the relation of the space-time metric and the curvature. I have determined the space-time metric, g_(alpha beta), but I am unsure as how to go from the line element ds^2 = [ 1 + (dz/dr)^2] dr^2 + r^2 dtheta^2 and the space-time metric g to the...

Decades have passed since the first idea of General Relativity arose in the mind of Einstien. Surely development of the GR must have taken place during these years. May anyone one update me about these development that took place since the late past.oo):w

Hello, This spring, I will have the opportunity to do a one-on-one independent study in math or physics. I've narrowed down my choices to differential geometry and general relativity. I'm thinking about the future here- will studying general relativity this spring better prepare me for...

I was recently exploring time dilation from Gravity and from velocity and I came up with an interesting derivation that I have not seen before. I was wondering if there is a paper published showing these relationships like this before and where I could find it? First you start with the...

So I recently watched the new movie Interstellar, and I've been inspired to do some more general relativity. At one point in the movie they mention that 1 hour on a planet orbiting a black hole is 7 years back on Earth, and so I decided my first project would be to figure out exactly how close...

I can fairly understand the concept of gravity as a curvature in space time in general relativity, but so far I could not understand completely the tidal forces explained by the curvature of spacetime. When the moon is on one side of the earth, the oceans on this side come closer to the moon...

Consider a flat Robertson-Walker metric. When we say that there is a singularity at $$t=0$$ Clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is "another coordinate system" in which the corresponding metric has no singularity as we...

Hello! I hope I am posting this in the right thread! As I was solving a problem in general relativity, my final answer needs to get a little fancier. So my final answer was as follows: $$ (\bar{U}{U})^3 (\epsilon_{ijk} \frac{d\omega^i}{dx^k} \theta^k) \wedge (\epsilon_{ijk}...

I'm curious about time dilation sizes of below 4 situations. Please assume I'm observing the situations far away in zero gravity. And please ignore all SR effects, just focus on GR. http://dishdev.me/data/timedilationq.png Equivalence Principle says acceleration and gravitational fields can...

If you look at Newtonian gravity, there is no major deal with coordinate systems. I am guessing we use coordinate systems because in general relativity we think of coordinate systems as different frames of references and that all frame of references must have the same laws of physics. Is that why?

Is there any book or reference perhaps on string theory or superstring theory or even advanced general relativity that treats the Israel Wilson Perjes metric using the tetrad formalism in details, i.e, 1-forms and so? (Not spinors methos) I have ran across many papers that just place the spin...

We have this stationary metric, $$ds^2 = e^{2U}(dt+\omega_idx^i)^2 -e^{-2U}dx^2$$ The book wrote down the spin connections of this: $$ \omega^{0i}=\partial_ie^{U}e^0 +e^{3U}\partial_{[_i\omega _k]}e^k $$ and $$ \omega^{ij}= e^{3U}(\partial_{[_i\omega _j]}e^0-\partial_{[_ie^{-2U}\delta_j]k} )$$...

The question that ponders upon the thought if the speed of light really is constant is a fairly common question. However, I was wondering about something and MAYBE this can provide some backup to the theory that the speed of light isn't constant, please point out any mistakes I make in stating...

I am thinking of taking a course on General Theory of Relativity in the next semester of college. My major is in aerospace engineering. I have already completed courses on Calculus, Differential equations, Linear Algebra, and also have a fair bit of idea about tensor calculus. What other prior...

hello, I would like to learn general relativity. To understand general relativity, do I need to understand the math on a rigorous level? (the way mathematicians understand the math) . What math do I need? Can you suggest me some math/general relativity books? Thanks and sorry if my english...

Hi. In class, the professor has tried to derive the equation by using the principle of least-action. (But not yet completed. Maybe next class...) However I heard this method is used by Hilbert, who had derived the equation 5 days before Einstein derived it. Then, what method did Einstein use...

Whenever the twin paradox in GR seems to be discussed, it always seems to be done in the presence of a large mass such that the twins can be considered as test particles moving in some metric. I was wondering whether the same problem could be generalised and be proposed in completely empty...

As some may know, I have been studying the Morris-Thorne wormhole metric for quite some time now. ds2= -c2dt2 + dl2 + (b2 + l2)(dθ2 + sin2(θ)d∅2) Now, from this space-time interval, it is easy to see how I would deduce the following metric tensor: g00= -1 g11 = 1 g22= (b2 + l2) g33= (b2 +...

I found a new book on The Science of Interstellar by Kip Thorne https://www.amazon.com/dp/0393351378/?tag=pfamazon01-20 What caught my attention was a photo of John Wheeler at the black board teaching about black holes. You could see the incredible detail in each pane of the board almost like...

Just finished Leonard's lections on general relativity. Thriving with questions...

I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal representation of the universe: "Neither does the theory of relativity, Bohr argued, provide us...

Just a quick question. I've recently thought about the various equations I'm learning about calculating velocity or vertical motion and have wondered that sense these equations are using Gravity as a constant force (9.8m/s^2) Is it not true that Einsteins' theory would denounce this idea and...

Homework Statement An observer is orbiting at a radius r = 3GM, \theta = \frac{\pi}{2} and \phi = \omega t where w is constant. The observer sends a photon around the circular orbit in the positive \phi direction. What is the proper time \Delta \tau for the photon to complete one orbit...