Energy-momentum Definition and 100 Threads

why general relativity can't define any tensorial expression for Gravitational energy momentum density ?

Homework Statement Derive Tμν=FμλFνλ-1/4ημνFλθFλθ From \mathcal{L}=1/4F_{μν}F^{μν}+A_μJ^μ Homework Equations Above 3. The Attempt at a Solution The first term of the given equation and the second term of the equation to prove are i believe the same.i know, Jμ=\partial_νF^{μν}...

I am a bit confused here. In the Einstein Field Equation, there is a tensor called stress-energy tensor in wikipedia and energy-momentum tensor in some books or papers which is $$T_{\mu\nu}=\frac{2}{\sqrt{-g}}\frac{\delta(\mathcal{L} \sqrt{-g})}{\delta g_{\mu\nu}}$$ Is it equivalent to the...

Say we were given an expression for the energy-momentum tensor (also assuming a perfect fluid), without getting into an expression with multiple derivatives of the metric, are there any cases where it would be possible to deduce the form of the metric?

Hi everyone, While reading http://relativity.livingreviews.org/Articles/lrr-2011-7/fulltext.html reference I bumped into a result. Can anyone get from Eq.19.1 to Eq.19.3? I've also been struggling to get from that equation to the one before 19.4 (which isn't numbered)...anyone? Thank...

Hello everyone, I was studying how to define, formally, an energy-momentum tensor for a point particle. I was reading this two references:http://academic.reed.edu/physics/courses/Physics411/html/page2/files/Lecture.19.pdf , page 1; and http://th-www.if.uj.edu.pl/acta/vol29/pdf/v29p1033.pdf...

Hi everyone, It's not a real homework problem, but something I am trying to do that I haven't found in the literature. I am still stating the problem as if it was a homework Homework Statement Consider a FRW Universe. That is, ℝ x M, where M is a maximally symmetric 3-manifold, with a RW...

Homework Statement I'm following the derivation of finding the energy flux of a gravitational wave propagating along the z-axis where they use the energy-momentum pseudotensor to achieve this, but I can't seem to get an answer that matches theirs. Homework Equations We are given a general...

Dear PF, I am a little bit confused could you pls help me ... Suppose I a have a scatering or conversion of two particles via graviton propagator. Graviton propagator couples with energy-momentum tensor of matter fields. So can i assume that vertex to which graviton propagator is coupled...

Hi there, I'm having a problem calculating the energy momentum tensor for the dirac spinor \psi (x) =\left(\begin{align}\psi_{L1}\\ \psi_{L2}\\\psi_{R1}\\ \psi_{R2}\end{align}\right)(free theory). So, with the dirac lagrangian \mathcal{L}=i\bar{\psi}\gamma^\mu\partial_\mu\psi-m\bar{\psi}\psiin...

Homework Statement Show that the energy-momentum relationship, E^2 = p^2 * c^2 + (m*c^2)^2, follows from the expressions E = (gamma)*m*c and p = (gamma)*m*u where (gamma) = 1 / sqrt(1 - (u^2)/(c^2)) the lorentz transformation factor. m is the rest mass. c is the speed of light u is the...

The energy-momentum tensor for a perfect fluid is T^{ab}=(\rho_0+p)u^au^b-pg^{ab} (using the +--- Minkowski metric). Using the conservation law \partial_bT^{ab}=0, I'm coming up with (\rho+\gamma^2p) [\frac{\partial\mathbb{u}}{{\partial}t}+ (\mathbb{u}\cdot\mathbb{\nabla})\mathbb{u}]=...

Hi guys, can you help me with this? I'm supposed to calculate the energy momentum for the classic Maxwell Lagrangian, \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} , where F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu with the well known formula: T^{\sigma\rho}=\frac{\delta\mathcal{L}}{\delta...

Homework Statement Arrive at the orthogonality relation {T^{\mu}}_{\alpha}{T^{\alpha}}_{\nu} = K{\delta^{\mu}}_{\nu} and determine K. Homework Equations T_{ij}=T_ji} The Attempt at a Solution {T^{\mu}}_{\alpha}{T^{\alpha}}_{\nu} = {T^{\mu}}_0{T^0}_{\nu}+ {T^{\mu}}_i{T^i}_{\nu} I am not...

How do you prove that Maxwell's energy-momentum equation is divergence-free? I don't know whether or not I have to use Lagrangians or Eistein's tensor, or if there's a simlpler way of expanding out the tensor.. ∂_{\mu}T^{\mu\nu}=0...

How do you prove that the energy-momentum tensor is divergence-free? ∂μTμν=0

My first question, so sorry if it's in the wrong forum. I'm trying to understand the Newtonian weak field approximations to general relativity. I can't see why, if the Schwarzschild metric (which can describe the gravitational field around the Sun) is a vacuum solution (T_{\mu\nu}=0 ) , do...

I have studied Jackson, Landau, and Barut textbooks on electrodynamics, together with Weinberg's Gravitation and Cosmology textbook, and I find that the usual action S = S_f + S_m + S_{mf} is inconsistent and not well-defined. For instance, what is the meaning of S_f? A free-field term? Or...

Hello, I was wondering, since gravitational waves carry energy-momentum, would it be possible to find them in regions where the components of the metric tensor vanish? That is to say, empty space (non-quantum) is described by a vanishing energy-momentum tensor - but then, if gravitational waves...

Let's discuss only classical fields and particles. For fields, E[SIZE="1"]2=p[SIZE="1"]2+m[SIZE="1"]2 applies only if the field is free. In the presence of sources, we have to use the energy-momentum tensor. For particles, does E[SIZE="1"]2=p[SIZE="1"]2+m[SIZE="1"]2 apply only when they...

Hi This might be a stupid question, so I hope you are patient with me. When I look for the definition of the energy-momentum tensor in terms of the Lagrangian density, I find two different (?) definitions: {T^\mu}_\nu = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\partial_\nu...

I've been comparing various books, including these: Mermin, It's About Time Takeuchi, An Illustrated Guide to Relativity for possible use in a gen ed course on relativity. It's cool to see that there are so many books out there now that aren't just replaying Einstein's 1905 postulates with the...

Okay so I have: Eqn1) Tij=\rhouiuj-phij = \rhouiuj-p(gij-uiuj) Where Tij is the energy-momentum tensor, being approximated as a fluid with \rho as the energy density and p as the pressure in the medium. My problem: Eqn2) Trace(T) = Tii = gijTij = \rho-3p My attempt: Tr(T) = Tii...

Homework Statement The problem is conveniently located here: http://www.dur.ac.uk/resources/cpt/graduate/lectures/mscps.pdf Problem no. 31. There's even a solution, here: http://www.dur.ac.uk/resources/cpt/graduate/lectures/grsolns.pdf However, I don't understand the solution...

Does anyone know of a derivation of the energy-momentum relation that does not make use of relativistic mass? In other words, a derivation that only uses invariant mass.

Hi all - first post at PF. As a 'science enthusiast' with no training in the tensor math of GR, was initially bewildered by the common assertion that still hypothetical 'dark energy' would act as a source of 'negative gravity' despite having positive energy density. Finally grasped that pressure...

Electrodynamics force is f_i=F_{ik}j^k=F_{ik}\partial_j F^{jk}. I claim that the only way to obtain the Maxwell energy-momentum tensor T_i^j=-F_{ik}F^{jk}+\delta_i^jF_{kl}F^{kl}/4 is to write the force as a divergence: f_i=-\partial_jT_i^j.

I'm studying General Relativity and facing several problems. We know that energy-momentum must be Lorentz invariant in locally inertial coordinates. I am not sure I understand this point clearly. What is the physics behind?

How do I get from the Energy-Momentum equation of a particle to its Stress-Energy equation? By way of introducing the energy-momentum equation: For a single particle, in units where c=1, a relationship between mass, energy and momentum appear as a direct result of the 4-velocity: m^2 =...

Hi all, In Polchinski's string theory text he asserts (volume 1, section 3.4) that the trace of the energy-momentum tensor of a classically scale -invariant theory becomes proportional in the quantum theory to the beta function of the coupling, as a general point of QFT. This makes a kind of...

Restmass: m_0 = \sqrt{\frac{E^2}{c^4} - \frac{p^2_x}{c^2} - \frac{p^2_y}{c^2} - \frac{p^2_z}{c^2}} Relativistic mass: m_{rel} = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} \sqrt{m_{rel}^2 - \frac{m_{rel}v^2_x}{c^2} -\frac{m_{rel}v^2_y}{c^2} -\frac{m_{rel}v^2_z}{c^2}} = \sqrt{\frac{E^2}{c^4}...

Okay, these questions aren't completely about the Higgs, but it is a good starting point / explicit example. After spontaneous symmetry breaking occurs, such that the vacuum state itself no longer has the symmetry of the Lagrangian, will there always be something equivalent to a Higgs (a...

Not sure if this is the right place to ask, but this doubt originated when reading on string theory and so here it goes... The general canonical energy-momentum tensor (as derived from translation invariance), T^{\mu\nu}_{C} is not symmetric. Also, the general angular momentum conserved...

Homework Statement A positron of rest mass me, kinetic energy equal to its rest mass-energy, strikes an electron at rest. They annihilate, creating two high energy photons a and b. The photon a is emitted at the angle of 90 degress with respect to the direction of the incident positron...

Hi, I believe you can use the "energy-momentum tensor" to express the conservation of both energy and momentum for fields (\partial_{\mu} T^{\mu \nu} = 0). But I'm wondering: why's a tensor needed, specifically, to describe this conservation of energy and momentum for fields? For particles, I...

Hi, I am trying to quickly resolve a fairly basic question that cropped when considering relativity. Classically, the total energy of a system is often described in term of 3 components: Total Energy = Rest Mass + Kinetic + Potential If I ignore potential energy, i.e. a particle moving in...

Hi I have a small subtle problem with the sign of the energy-momentum tensor for a scalar field as derived by varying the metric (s.b.). I would appreciate very much if somebody could help me on my specific issue. Let me describe the problem in more detail: I conform to the sign convention...

>From a seminar, I heard that energy-momentum relation (E^2=m^2+p^2) is modified by UV/IR mxing. In other words, the speaker claimed that the lowest energy is achived not by zero momentum, but by non-zero momentum. Could somebody refer me to a relevant paper? Thanks in advance Youngsub

A mentioning about virtual particle problem in my other thread just reminded me of some thoughts, which I now succeeded putting together. When calculating cross sections in QFT, we encounter terms like this \langle 0|a_{\textbf{k}'} a_{\textbf{p}'} a^{\dagger}_{\textbf{p}_1}...

I was wondering if someone could clarify something that I read in a book (Nakahara's book on Geometry, Topology, Physics). In the section on the Einstein-Hilbert action, the author defines the energy-momentum tensor as \delta S_M = \frac{1}{2} \int T^{\mu \nu} \delta g_{\mu \nu} \sqrt{- g} d^4...

...for a point particle is a 4-vector. Consequence : E^2-c^2(\vec{p})^2 is an invariant Nevertheless, for a system of particles, the energy momentum is not a 4-vector. See here. Hence (\Sigma E)^2-c^2(\Sigma \vec{p})^2 is not an invariant. See here

How is derived the classical energy-momentum relation, E = p^2/2m? Thanks!

I was just wondering why what I've done in a spec rel question is wrong. Homework Statement A particle of mass m is traveling at 0.8c with respect to the lab frame towards an identical particle that is stationary with respect to the lab frame. If the particles undergo an inelastic collision...

Homework Statement A roller coaster is lifted up 50m above the ground to the top of the first hill and then glides down around the track at the bottom. If it had a velocity of 3.0 m/s at the top of the lift and loses 10% of its total energy to friction as it glides down, what is the roller...

I'm using a following notation. (v^1,v^2,v^3) is the usual velocity vector, and (u^0,u^1,u^2,u^3) = \frac{1}{\sqrt{1-|v|^2/c^2}}(c,v^1,v^2,v^3) is the four velocity. So a energy-momentum tensor of dust is T^{\mu\nu} = \rho_0 u^{\mu} u^{\nu} =...

We have the metric ds^2=-e^{2\Phi}dt^2+e^{2\Lambda}dr^2+r^2d\Omega^2, and the energy momentum tensor takes the form t^{ab}=(\rho+p)u^au^b+pg^{ab} where the 4-velocity is u=e^{-\Phi}\partial_t, and \Phi and \Lambda are functions of r only. I'm asked to show that the ebergy-momentum...

Does anyone know how you find the length of the energy-momentum four-vector for a system of particles? p_mu=(E/c,p) where length is: length(p_mu)=-(E/c)^2+(p)^2 Do you first add the corresponding vector elements then find the length OR find the length of each particle first then sum...

How can you go about and prove the following : The energy-momentum tensor for any classical field theory = -2 X the functional derivative of the action with respect to the metric tensor.

Is it correct that the only way to have a theory of gravitation that fulfills the equivalence principle is to make use of a tensor as the source of gravity (and not a scalar or a vector, for example)? How can this be proven?

Mass-energy equivalence is fundamental in relativity, but it seems like energy and momentum are also different aspects of the same thing. They've each got very important conservation laws. In SR, the space coordinates of the four-momentum give the momentum while the time coordinate gives...