field equations Definition and 105 Threads

There seems to be an emphasis in several books on general relativity that the metric (components) in itself does not reflect anything physical, only our choice of coordinates. On the other hand it can seem like the authors, instead of being true to this, treat the metric (components) as...

I'm reading Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carrol and in the chapter on gravitation, he derives the Einstein Field Equations. Here is the part I don't get. He starts with the equation R_{\mu\nu}-\frac{1}{2} Rg_{\mu\nu}=\kappa T_{\mu\nu} Wher R_{\mu\nu}...

I am working on a novel that uses 'gates' that for lack of space here let’s just call worm holes (any excuse works for this question). But these gates cannot bridge to each other if located in a region of space that is warped too much. So I'm looking for a proportional answer, not a calculated...

Hi all. I've been trying to study microwave and electromagnetic engineering . I'm not sure how I should interpret j in some of the field equations. For example, for the field equations for a rectangular waveguide resonant cavity are: E_{y} = E_{0} sin\frac{\pi x }{a} sin \frac{l \pi z}{a}...

Hi everyone, Say that one can separate the metric of a space time in a background metric and a small perturbation such that g_{\alpha \beta}=g'_{\alpha \beta}+h_{\alpha \beta}, where g'_{\alpha \beta} is the background metric and h_{\alpha \beta} the perturbation. Computing the christoffel...

I am trying to prove a concept that was presented in my course but I am having a bit of an issue with understanding the final result. The concept was that in 3 dimension the vanishing of the Riemann tensor leaves only the trivial solution for the vacuum equations. I started by subbing Eq.(1)...

Did anybody else hear the news? A recent paper examines the derivation of Einstein's field equations and proposes that the original assumption of a divergence-free energy-momentum tensor may not be valid anymore due to the discovery of dark matter and dark energy. The authors derive new field...

I have seen and read a few different versions of the Einstein field equations (EFE). For example; R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = - 8\piGT_{\mu\nu} , R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R + g_{\mu\nu}\Lambda = \frac{8 \pi G}{c^4}T_{\mu\nu} , and 8\piT_{\mu\nu} = G_{\mu\nu} So which one is...

Hi all, I have been trying to solve the Einstein Field Equations for its (0,0) component. So I have got that (c=1) Einstein Tensor (upper,0,0)=8*pi*G*T(upper,0,0) Now, let's see what T (0,0) really is. It is energy density, right? So According to famous E=mc^2 the energy density is the same...

Or is my brain to small ? Personally i don't like the field equations, because they are complicated. Richard Feynman would say to this, if you don't like it go to another universe where the laws of nature are much simpler. But then again on sub-atomic level symmetry was a good guide ... e.g...

I was working on a problem the other day involving the Tensor versions of the Einstein Field Equations where I defined a metric (minkowski) and then defined a Stress-Energy-Momentum Tensor and solved for the corresponding Ricci curvature Tensor, now that I have all of this solved what do I do...

I'm a bit confused by the following: We can derive the equation of motion for a particle traveling on a timelike worldline by applying the Euler-Lagrange equations to the Lagrangian \mathcal{L}=- g_{\mu \nu}(x(\tau)) \frac{d x^\mu}{d \tau} \frac{d x^\nu}{d \tau} However, to derive the...

I was wondering if equations similar to Einstein's field equations show up anywhere else? I have a degree in physics but a guilty pleasure of mine is watching those popular physics documentaries, and I invariably grit my teeth when they use the rubber sheet analogy to explain gravity...

Hi all! When we talk about the Einstein Field equations. What do we mean with "extremal proper time" or "extremal path"? Why "extremal" ? and why "proper" ? and why do we need to introduce the concept of "geodesic" ? Cheers

Can somebody explain a little bit about how to actually use Einstein's field equations to solve for particle locations? Relevant information: parentheses are sub-scripts R(uv)-1/2guvR+guv(cosmological constant sign)=(8piG/c^4)T(uv) where R is the Einstein Tensor R is described by...

Homework Statement Given an arbitrary curve or surface with a total charge of Q, find the vector equation for the electric field at any point in space. Homework Equations dE = 1/(4πε₀) dq /r2 The Attempt at a Solution Problem 1 Take the unit circle on the plane, for example. Find the...

You can rewrite Maxwell's equations using d'Alembertian operator on quaternions. Can something similar be done for Einstein's Field equations and is there an advantage in doing so? Will this help in finding solutions to the equations or e.g. calculation of proper time,proper distance? Will...

Can one deduce from the einstein field equations: -Conservation of mass -Conservation of energy -Conservation of mass-energy -Conservation of linear momentum -Conservation of angular momentum -Principle of least action ? And does curvature of space-time has a "potential" on certain...

Looking at Lagrangians and field equations for different spin all the derivations seem to lack a common basis; they appear to lack any deep relation. Is there a unique way to understand the different forms like Klein-Gordon, Dirac, Maxwell (Yang-Mills), etc. from a common basis which is valid...

Suppose there is a solution to the field equations with the Einstein Tensor = 1: Gtt = 1 and/or, Gxx = Gyy = Gzz = 1 This would leave for the stress energy tensor: T = 1 / 8 pi G Now for stress, it seems to get physical units of pressure, you would apply: Txx = Tyy = Tzz =...

Hi there, physics lovers. I'm studying field theory. So far, so well. I got it with the lagrangian density. I understood it. But then I DIDN'T FIND stuff about the Hamiltonian density. I couldn't find anything in Landau-Lifgarbagez series, and that makes me worry. I've been looking in the...

Homework Statement Homework Equations E=ke*q/r2 The Attempt at a Solution See screenshot. The angles are correct, however I can't get the equation right for either part. I understand they should be different since one is force and the other electric field, I thought that should be...

Einstein wrote in his book The Meaning of Relativity of 1921 p48 when deriving Field Equations : " We must next attempt to find the laws of gravitational field .For this purpose ,Poisson's equation of the Newtonian theory must serve as a model.'' I have three question: 1\ How to derive...

So I am an engineering graduate trying to teach myself some general relativity. I have tried to solve the Einstein Field equations for a wormhole metric and some others. After pages and pages of calculating Christoffel Symbols, Riemann Tensors, Ricci Tensors and Scalars, and so on, I end...

For Minkowski spacetime, the metric is: ds^2 = -dt^2 + dx^2 + dy^2 + dz^2 I have read there is a solution when the time dimension is "rolled" into a cylinder forming a closed timelike curve. So the BC is t -> [0,T] with t = 0 identical with t = T. The Field Equation is: Rab - 1/2...

1) What exactly does the metric tensor expand into? Since it describes general space-time, shouldn't it be more like a vector like R = √(x^2+y^2+z^2) Why even should we use tensors in relativity when we can just stick with vectors? 2) Are the equations all theoretical? Have they been...

no. of field equations and components or Riemann tensor?? Someone was trying to explain to me about curvature in space. From what I got from what they were saying doesn't make sense to me. I'm not sure I understand what the number of components, N, of R\alpha,\beta,\gamma,\delta when compared...

Einstein Field Equations? I have not been able to comprehend the Einstein Field Equation, the Stress Energy Tensor, the Ricci Tensor, the Einstein Tensor, and Christoffel Symbols. Though I am reasonably proficient at working with nested loops in programming, and I have a rudimentary knowledge...

Why should we trust the Reissner–Nordström solution of charged black holes? It relies on coupling between Einstein tensor and EM stress-energy tensor, which has NO experimental support whatsoever. Is there any chance we can test this?

Experimental "measurement" of Einstein's Field Equations The question is essentially: What if we took a strictly experimentalist view, and considered a phenomenological model for gravity that is a "generalization" of EFE: R_{\mu \nu} - C_1\ g_{\mu \nu}\,R + C_2\ g_{\mu \nu} \Lambda = C_3\...

I have been working through a relativistic gravitation book ("Gravitation and Cosmology" by Stephen Weinberg) and decided to circle back to the early tensor work in chapter two and just work out the basic tensor math to make sure that I have a feel for how it all goes together. Right at the...

I understand the difference betw mathematical and physical pi. I also understand that in non-Euclidean space the value of pi would differ depending on a surface's deviation from flatness. But is there a different symbol for physical pi, to distinguish it from mathematical pi? Because I...

Einstein-scalar field action --> Einstein-scalar field equations Dear friends, Just a small question I do not know how to derive. From the Einstein-scalar field action defined by S\left( {g,\psi } \right) = \int_{} {\left( {R(g) - \frac{1}{2}\left| {\nabla \psi } \right|_g^2 - V\left(...

Where can I find the paper of Hilbert's derivation of General Relativity's field equations? I heard it is more elegant than Einstein's. Thanks

can any 1 tell mme the derivation of [SIZE="4"][FONT="Impact"]Einstein's field equations? please

Hi all, I'm following along the derivation of the field equations for f(R) gravity, and there's one step I don't understand entirely. There's just something in the math that's eluding me. So wiki has a pretty good explanation...

Hi, I don't remember how this came up, but I stumbled across a "wrong" solution to Einstein's field equations that involved a spinning universe and being able to see one's future. Does anyone know what I am thinking of?

Can someone explain the equation G_{\mu\nu}+\Lambda g_ {\mulnu}={8\ pi G\over c^4} T_{\mu\nu}\ by Albert Einstein?

Einstein's "The Field Equations of Gravitation" Paper I'm trying to find a translated copy of this paper - but i can't find one anywhere! The 1905 papers are all over the place; i thought the this would be similar. Does anyone have a copy, or recommendations on where to look? Thanks...

I realized that there is no strict derivation of Einstein's Field Equations. However I found no 'derivation' that make me feel 'comfortable' and 'logical'. Could anyone post a 'derivation' with smooth logical sense ? Thank you.

this is a question more about the history of the field equations, but did Einstein get his field equations originally by varying the Einstein-Hilbert action or was it that the field equations was were found first then the they can also be shown by the varying the action. my feeling is that its...

Homework Statement Let F be a field. For any a,b \in F, b\neq0, we write a/b for ab^-1. Prove the following statements for any a,a' \inF and b,b' \in F\{0}: i.) a/b = a'/b' if and only if ab' = a'b. ii.) a/b + a'/b' = (ab' + a'b)/bb' iii.) (a/b)(a'/b') = (aa')/(bb') iv.)...

Are the phrases "Linearized gravity", "Linearized Einstein Field Equations", "GEM (gravitoelectrodynamics)", all referring to mathematically equivalent approximations of Einstein's full non-linear field equations? If not, could someone tell me what order (in some rough sense) these would be...

Hello, As with a lot of people, I have been excited and fascinated by the field equations Einstein described, revealing the curvature of spacetime. I would like to create a computer simulation which simulates the effects of the Einstein Field Equations, in other words, the curvature of...

In the usual way to do QFT, we find the Green functions to the quadratic part of the lagrangian (usually with Feynman boundary conditions), and use this in the computation of n point (usually time ordered) correlation functions. Suppose one manages to solve instead the full nonlinear equation...

Suppose a spaceship is leaving earth, moves close to the speed of light, passes regions of strong gravitational fields, etc., then the Einsteins Field Equations (EFE) should be able to predict the path of the spaceship with great precision. My question is how we specify the position of the...

Einsteins field equations are nonlinear but I guess that nobody has already found solutions to the full nonlinear equations (because of course it is very hard to do so). Nevertheless, such solutions could (I think) hold a number of surprises. Instead of linear gravitational waves, one could...

could soemone give me a site, or let me know of a book that gives the field equations in the context which Einstein presented them, along with his discussion of their implications?

I am only just starting to realize that there is a correspondence between quantum field theory and Einsteins field equations. In QFT the approach is to write the Lagrangian and then to solve the Euler Lagrange equation to obtain the equations of motion of the field. In GR it seems that...

Using the equation E= (kq)/(R)^2 in the r direction. I am confused on when to make the vector negative in my equations. For instance if you had a charge on x=0 and x=5 (on the x axis) and then you want to find the field at point (1,1) or something like this.