General relativity Definition and 999 Threads

I am trying to find a derivation of gravitational redshift from a static metric that does not depend on the equivalence principle and is not a heuristic Newtonian derivation. Any suggestions?

PeterDonis submitted a new PF Insights post The Schwarzschild Geometry: Part 4 Continue reading the Original PF Insights Post.

I have a few conceptual issues following a standard thought experiment to argue why light bends in a gravitational field and I'm hoping I can clear them up here. Consider an observer in a lift in free-fall in a uniform gravitational field and an observer at rest in the uniform gravitational...

PeterDonis submitted a new PF Insights post The Schwarzschild Geometry: Part 3 Continue reading the Original PF Insights Post.

PeterDonis submitted a new PF Insights post The Schwarzschild Geometry: Part 2 Continue reading the Original PF Insights Post.

PeterDonis submitted a new PF Insights post The Schwarzschild Geometry: Part 1 Continue reading the Original PF Insights Post.

Is it correct, at least in the context of general relativity, to say that in a coordinate basis, the inner product between space-like basis vectors will be 1, and in a non-coordinate basis the inner product will be defined by the corresponding component of the metric? Can I take this conditions...

Is there a formulation of any of the relativity theories in terms of complex analysis? As in - I imagine - every event would be a complex number in a complex field.. or something as such..

I understand that General Relativity can make a difference between a spinning and non spinning mass thus can make better prediction for planetary orbits for example. The effect is frame dragging. However if we simulate a Newtonian gravitation and instead of representing a planet as a sphere...

In my Google searchs and by reading threads on this forum I've seen that the books people most recommend on general relativity are Graviation, by Thorne, Wheeler and Misner, Wald's book and Weinberg's book. I'm in the first year to get a bachelor degree on physics and I could read any of these...

I've heard that unlike Special Relativity, General Relativity claims that you can' say any reference frame is better than another frame, including frames in which Newton's Laws don't hold. I've seen debates about this specifically in the context of geo/helio-centrism. From what I understand...

I have to do a project on wormholes as solutions to the EFE, but I'm only and undergrad and have not yet taken any GR classes. I found a paper by Michael Morris and Kip Thorne with a derivation of a simple wormhole (many assumptions), but because of my lack of experience I can't tell what the...

Hi. (I'm sorry for my poor English.) I'm looking for a good book on General Relativity, specially on Black Holes and Graviational Waves. I got Schultz book once ago, but it has a fuzzy notation and does not deal with the math as I suppose to. I know the basics of Differential Geometry, Topology...

Homework Statement Suppose we have a covariant derivative of covariant derivative of a scalar field. My lecturer said that it should be equal to zero. but I seem to not get it Homework Equations Suppose we have $$X^{AB} = \nabla^A \phi \nabla^B \phi - \frac{1}{2} g^{AB} \nabla_C \phi \nabla^C...

I'm trying to understand how the various EM tensors work in General Relativity. The only source I've found is https://en.wikipedia.org/wiki/Maxwell%27s_equations_in_curved_spacetime, but there are two things I don't get. Why do they use ordinary partial derivatives instead of covariant ones...

Tidal Forces: "It arises because the gravitational force exerted by one body on another is not constant across it". which implicitly implies that the acceleration is not constant on that body. Equivalence Principle: "weightlessness sensation occurs when one free falls in gravity" - which...

Hello I have not understand this.

I'm currently taking a course in Theoretical Mechanics, which is a prerequisite to General Relativity, which I'm very much looking forward to taking. However, I'm not that good in mechanics, and Real Analysis seems to be more straightforward than even the first course in Mechanics. I'm quite...

If I take a spaceship and park it near the event horizon of a black hole and then measure the age of the universe by observing SNe Ia, then travel back out to normal space (no gravitational forces, at rest with respect to CMB), will the dates agree? That is, if the measured age of the universe...

Hello! I have a question that has been bothering me since I first started learning about Special Relativity: Given only the Minskowskian metric and/OR the spacetime interval, how can one reach the conclusion that the speed of light is invariant for every observer and how can one conclude that it...

Hello! What book should I use as an introduction to General Relativity? Something that includes an introduction of the math behind GR (tensors for example) would be much appreciated. Thank you!

I'm confused about how the predictions of this graph were formed. I have this formula: But the change in frequency per second is about : 2x 10^-12 which has a problem because when you multiply this by 10 years you don't even get a change of frequency of 1/1000 of a second and in the graph it...

I always hear that the two 'don't match' and disagree, but never in what... Someone mind explaining?

I'm looking for the distribution of all wavelengths (or frequencies) of light that a stationary observer would receive at his location (at ##r = 0## and time ##t_0##), from all light sources emitting a single wavelength ##\lambda_{\text{e}}## (or angular frequency ##\omega_{\text{e}}##). The...

How would one go about setting up the stress energy tensor for a particle, say an electron subjected to electric an electric field that makes the particle oscillate with frequency \omega?

Homework Statement What is the Schwartzchild metric. Calculus the 4-velocity of a stationary observer in this spacetime (u). Show that u2 = c2. Homework Equations Schwartzchild Metric d{s^2} = {c^2}\left( {1 - \frac{{2\mu }}{r}} \right)d{t^2} - {\left( {1 - \frac{{2\mu }}{r}} \right)^{ -...

In particular how does matter "clump" together to form stars and planets, and how do Galaxy/star systems form? For the latter question is the answer simply that near massive enough bodies, the spacetime curvature is significant enough that the geodesics within its vicinity are closed curves...

Homework Statement Below: Jac = Jacobian matrix; ξ = d/dφ for some continuous parameter φ which labels different points on the worldline. (I'm sorry for my poor English.) Consider a new coordinate system xµ' which differs from the original Cartesian coordinate system xµ; the Cartesian...

I have read this paper http://www.sciencedirect.com/science/article/pii/S1355219813000695 that the author try to said that einstein not believe that gravity is not cause the space time curvature. I want to know that this is true or not. Because when I have read about general relativity I always...

haushofer submitted a new PF Insights post General Relativity as a Gauge Theory Continue reading the Original PF Insights Post.

The material I am studying express the Ricci form as ##R = i{R_{\mu \bar \nu }}d{z^\mu } \wedge d{{\bar z}^\nu } = i\partial \partial \log G## where ##G## is the determinant of metric tensor, but I am not sure what does ##\log G## here, can anybody help?

Is it possible for enough energy to be dissipated in the form of gravitational radiation in a two-body system to allow for capture? From what I remember, you would need extremely massive bodies passing extremely close to each other: I'd like to know how massive and how close. It has been a few...

What does the dimensionless time in Rindler spacetime signifies? And how something dimensionless can be regarded as time and coupled up with proper distance in Minkowski spacetime? (Page 7: https://www.perimeterinstitute.ca/images/files/black_holes_and_holography_course_notes.pdf )

We have two theories namely,Quantum Field Theory which works very well at sub-atomic scales, and the General Relativity which works very well at very large scales.So, my question is where does statistical physics/mechanics fit in? What role statistical physics/mechanics play in today's modern...

Source: Basically the video talk about how moving from A to A'(which is basically A) in an anticlockwise manner will give a vector that is different from when the vector is originally in A in curved space. $$[(v_C-v_D)-(v_B-v_A)]$$ will equal zero in flat space...

What do you think about the work done by these Russians to give alternative formulations to General Relativity?

I know that in Special Relativity, proper acceleration is understood as: a*ga^3, where ga is the lorentz term and 'a' is coordinate acceleration. Is there a corresponding expression for proper acceleration within the various geodesics that result from solutions to Einstein's Field Equations? If...

Hi all, I fairly basic question about spin foam models in loop quantum gravity. I just want to verify that spin foams represent effectively represent all of spacetime (in a quantum form), and that the idea is that general relativity can be obtained in the classical limit? Not sure if that's...

I have in mind thought experiment where physicist is in elevator falling towards the Earth. Question would be if he is not allowed to look outside, how would he detect the presence of the planet? Let's not take in consideration tidal forces and assume he is taking local measurements during small...

For those who have read Schutz' book A First Course in General Relativity. Can this book be considered as a deep approach on the subject? Edit --- Do you think I will become a "expert" in general relativity just by reading books like this one I mentioned above? What time it take for learning...

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...