General relativity Definition and 999 Threads

If I want to take the wedge product of $$\alpha = a_i\theta^i $$ and $$\beta = b_j\theta^j$$ I get after applying antisymmetrization,$$ \alpha \Lambda \beta = \frac{1}{2}(a_ib_j - a_jb_i)\theta^i\theta^j$$ My question is it seems to me that antisymmetrization technique doesn't apply to the...

Hello Everyone, I have read many derivations of Einstein field equations (done one myself), but none of them explain why the constant term should have a $$c^4$$ in the denominator. the 8πG term can be obtained from Poisson's equation, but how does c^4 pop up? Most of the books just derive it...

Hello! I'd appreciate any help or pokes in the right direction. Homework Statement Show that a co-tensor of rank 2, ##T_{\mu\nu}##, is obtained from the tensor of rank 2 ##T^{\mu\nu}## by using a metric to lower the indices: $$T_{\mu\nu} = g_{\mu\alpha}g_{\nu\beta}T^{\alpha\beta}$$ Homework...

I've been learning the Israel formalism (see original article here) for thin shells. I think I understand the formalism well and how to do the matching given two manifolds (that are solutions of the Einstein's field equations - EFE). I've been studying several articles that use the matching...

Dear all, In one of his lectures,Prof. Susskind mentioned that the event horizon "bulges" forward to meet any incoming radiation or matter; and it is a property of Einstein field equations. I have not come across any such property, and if it exists, shouldn't it belong to the Schwarzschild(or...

This seems like a question that would be in the Relativity FAQ, but I didn't see it. Briefly: I've seen the claim made that there is plenty of observational evidence for the existence of black holes. But I don't understand how, from the outside, one can tell the difference between a black hole...

A map h: = T.(M) ---> T.(M) is defined by h(X) = X + g(U,X)U where U ε T.(M) is a fixed vector with g(U,U) = -1. i: Give an expression for the components h^i (sub) j (This is "h" with a superscript i and subscript j) of h regarded as a tensor type (1,1) ii: Prove that h^2 = h. Interpret h...

I have always been confused about time dilation in General Relativity. In the twins paradox, it is the traveling twin that ages slower. However, could you not just as easily say that it is the non-traveling twin that is moving away from the other? So why is it the traveling twin and not...

Alright, I'm rather new to General Relativity, and I'm getting confused with four momentum. Back in SR, p^α=mU^α, but, this relationship doesn't hold in curved space, does it? Because, now I'm seeing that four momentum is somehow a covector in GR, and p_0=-E, so the time component of the...

For example at very low speed (v<<c), in Special Relativity, we can approximate relativistic motion to Classical Newtonian motion. But in General Relativity, what situation can make there an approximation to Newtonian Gravity ( just like v<<c ) ? Thanks.

hi fellas, I want my undergrad thesis on general relativity. I need a good book on einstein field equations and its exact solutions to work with. also a book where are some solved problems and some exercises to guide me to right track any suggestions ? regards

Hi, I started reading General Relativity but concepts such as Lorentz transformations, rotations, tensors etc. are, at least in my opinion, poorly explained. Or perhaps the authors assume that the readers are already familiar with such maths? At any rate, I would very much like to read...

Has this idea been recognized outside Frankfurt? http://arxiv.org/abs/0812.1738 Pseudo-complex General Relativity Peter O. Hess, Walter Greiner (Submitted on 9 Dec 2008) An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new...

ok, so hear me out, please read the whole thing. so, next year I am going to a new school(tams) i will be starting my jr year in high school. and the classes are total only 4 hour long daily, that gives me a lot of free time. ive been reading a lot about quantum mechanics and some particle...

Hi all, I am really curious about the final state conjecture in general relativity, but I don't really understand it... There seems to be a really good explanation provided by Willie Wong here: http://math.stackexchange.com/questions/50521/open-problems-in-general-relativity however it is...

Hi, I am new here, I am no physicist and I'll admit have not read much on physics, but I do have a keen interest and a deep wanting to know answers and understand how and why things are the way they are. lately I've been reading a lot about General and Special Relativity, and time, I've always...

I'm reading a book about unification of general relativity and quantum physics. The author states that one of the axioms of GR is background-independence, meaning that space-time has no external reference points. All distances and motions in space-time are relative. On the other hand, the...

First I want to consider an example of 1D motion. Lagrange equation: $$ \frac{d}{dt} \frac{\partial L}{\partial \dot x} - \frac{\partial L}{\partial x} = 0 $$ If we transform $$L \rightarrow L+a$$ with a is constant, the equation of motion remains unchanged. This is global symmetry. To obtain...

SR is a theory based on flat space-time, and all of its effects are there in a flat space-time framework.My question is, how is SR compatible with GR, since GR uses curved space-time? Or to say it better how are time dilation, length contraction and relative simultaneity manifested in curved...

Hi, I'm going deeper in basics points on general relativity but, instead of swimming directly between the differential geometry, I'm trying to base my knowledge on strong physics bases first. I'm studying both on Wheeler's stuff ( I'm collecting almost all his books ), directly on Einstein's...

The concepts of general relativity seem to fit (sorta) well with quantum physics, but how does the quantum world fit with general relativity? Specifically, I'm wondering if entanglement has any grounds that you can derive from GR?

Hi, this might be a silly question, but it does confuse me when I read about general relativity. From what I know about quantum mechanics, a force always needs a force carrier. For example photons are force-carriers for electric or magnetic force; the so-called ‘gravitons’ are the force-carriers...

Theory of general relativity-- Falsifiable? "... Supposing that the bodies act upon the surrounding space causing curving of the same, it appears to my simple mind that the curved spaces must react on the bodies, and producing the opposite effects, straightening out the curves. Since action and...

In Padmanabhan's Theoretical Astrophysics by defining a ratio for comparing gravitational potential energy with rest-mass energy it is shown that if massive objects with M=10^33 gm are confined to small regions with R= 1km then we cannot use Newtonian gravity because the system has general...

How does General Relativity "contradict" quantum mechanics? I couldn't work out exactly where to post this. I've heard several times that QM and General relativity "contradict" each other and in certain extreme conditions this becomes a problem. Is this right? I've only heard this in very vague...

To my understanding General Relativity is a theory of geometry. Is it mandatory that the next step beyond GR also be a theory of geometry, or is there/could there be something else that is believed to give the same results without using geometry? I hope that makes sense.

Greetings, I've been learning about special relativity and most of the learning media included a part of general relativity. From that I learned that space-time is curved and orbits are nothing more than an object following a path in 4D. However I do not understand how those objects may rotate...

I have been teaching myself QFT and General Relativity. The mathematics of those fields is daunting, and I find that what I have come across is very difficult to master. Of course it will take work, but can someone recommend a good text for self-leaning differential geometry with application...

Hello! Could you, please, name some(if any exists) good reviews about building the general relativity? In all details: with attempts of building the vector theory of gravitation by Poincare; with long Einstein's efforts of building the scalar version; with prediction some of the effects, like...

Hello fellow PF go-ers I am having trouble with coordinates in curved space time lately, allow me to demonstrate my issue. Take the metric of flat space in spherical coordinates for example, a diagonal metric with values 1,r^2 and r^2sinΘ. It appears to me that only when we know that the Θ and...

Hello, I am learning General Relativity through some books like 'Gravity' by Hartle and through some other textbooks. All those books, do not speak of general relativity from the context of differential geometry. I have a fair amount of knowledge of calculus as well as set theory. My...

Hi, I decided to learn about relativity with this book, and I'm looking for people who would like to read it with me and discuss :thumbs:. Since I'm a little busy at the moment the pace will be quite slow, let's say about a chapter each two weeks (or more later for more advanced chapters)...

Hello, Can anyone help guide me in order to stabilize my General Relativity background. Little do I know about GR, I know the very simple basics! I feel that I need to start from the first beginning. ANy recommendations? How to start learning this on my own? Do I need to watch videos or read...

Homework Statement An observer falls radially inward toward a black hole of mass M, which is equal to 3 solar masses, starting with zero kinetic energy at infinity. How much time is measured by this observer as he travels between radii r1 = 6GM/c2 and the event horizon? Homework Equations...

I am writing a paper about SR and GR. I have the following: Special relativity deals with inertial reference frames and flat space. General relativity deals with accelerating reference frames and curved space. Inertial reference frames are only an approximation that applies in a region...

Hi guys... I was wondering if anyone have a sort of a summary of sign conventions in general relativity books. By convention I mean the definition of Riemann tensor, Ricci tensor and signs of stress-energy tensor and signs of einstein field equations for a given sign of metric tensor... I heard...

Hello all, I will preface this post with an apology for not putting it in the math/science learning materials section. This would have been the best place to post my question, but for some reason I can't post there. My question is the following: what depth of understanding must I have of...

There's an equation from Dirac's book on General Relativity that I don't get at all. It isn't derived; instead it's treated as almost self-evident, when it isn't. Dirac begins by defining ##p^\mu## to be the "mass 4-current" of a continuous distribution of matter (matter in this case really...

A satellite orbiting the globe at some 300 miles at 18000 mph. Does the clock on the GPS tick slower or faster than the same clock on Earth? 1) the clock is distant to Earth and is under less gravitational pull, resulting in time slowing down less than the Earth clock, therefore ticks faster -...

i have a question, that nobody seems to be able to answer : is math actually suited for reality ? Basically the idea is that reality seems to be granular, for example we have planks time. Usually the difference is so small, that is doesn't matter, but if you bring things like infinity into the...

Please view the following... http://www.wimp.com/visualizegravity/ This is the way scientists try to explain the warping of space to explain gravity effects between to objects. The very demonstration requires gravity to work! Why does one object track along the displaced track to begin...

Hi, In classical and quantum physics and even in special relativity, shifting the energy of a system by a constant (i.e. resetting the zero point) changes nothing in the dynamics and is not observable. In quantum field theory, we even have to shift by an infinite (but "constant") energy to...

In other words, can dark matter be reconciled with GR without drastically changing the idea that force is due to space-time curvature? and in the case of the standard model is there any thoughts of how the force of dark matter is transmitted via the exchange of a particle? It seems that this...

Hello, Can someone please help me to understand equation (10) from this article http://arxiv.org/abs/gr-qc/0607020. I do not see how does spherically symmetric tensor must (can) be written in that form. Thanks, Benjamin

Special and General relativity --Basic findings Hello All, Kindly note that it is not a home work. The Special Relativity (SR) and the General Relativity (GR) has some basic findings. I mean to say that say, SR:has some findings like: (a) The speed of light c is constant. (b) The...

The invariant mass of special relativity: m_0{^2} = E^2 – p^2 There doesn't seem to be any quantity with units of mass that is invariant in general relativity. Invariant mass loses significance, as other than an approximation where space-time is sufficient flat. But at the same time, mass is...

General relativity -- Conceptual question Hello, I have a conceptual question. May be I am sounding a little bit idiotic, so apologize for that. I believe, there is no harming in knowing that I am wrong. Einstein's general theory of relativity describes gravity as a geometry of space...

Well, here's the scenario I am particularly curious about: A riffle barrel and a laser point directly towards a target some distance away. Now, General relativity says that the bullet and the light experience the same downward acceleration during horizontal travel, yet the bullet hits...

Hi everyone, I've been reading posts here occasionally, and have been impressed with the amount and quality of knowledge that is being shared. I've just registered, and as my first thread I thought I would post some questions / thoughts that have puzzled me for a long time, related to...

I've been watching leonard susskind's lectures on general relativity on youtube, I'm now at the fifth of them. It is my first exposure to general relativity and so far the lectures are pretty easy to follow. So my question is this, to anyone who has had more exposure to the subject: Do you...