# What is Energy-momentum tensor: Definition and 59 Discussions

The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. This density and flux of energy and momentum are the sources of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.

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11. ### I Energy Density in SR Energy-Momentum Tensor

In Special Relativity I'm given the energy-momentum tensor for a perfect fluid:$$T^{\mu\nu}=\left(\rho+p\right)U^\mu U^\nu+p\eta^{\mu\nu}$$where ##\rho## is the energy density, ##p## is the pressure, ##U^\mu=\partial x^\mu/\partial\tau## is the four-velocity of the fluid. In the...

36. ### Deriving the Metric from the Energy-Momentum Tensor

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?
37. ### Energy-Momentum Tensor for a particle

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...
38. ### Proving Homogeneous & Isotropic FRW Universe Energy-Momentum Tensor

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...
39. ### Graviton Propagator and energy-momentum tensor

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...
40. ### Energy-momentum tensor for the Dirac spinor

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...
41. ### Deriving the Navier-Stokes equation from energy-momentum tensor

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}]=...
42. ### Calculating the energy-momentum tensor for Maxwell Lagrangian

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...
43. ### Relativity energy-momentum tensor

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...
44. ### Divergence of Energy-momentum Tensor

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...
45. ### Divergence of Energy-momentum Tensor

How do you prove that the energy-momentum tensor is divergence-free? ∂μTμν=0
46. ### Value of energy-momentum tensor in weak field approximations

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...
47. ### What is the electrodynamic action and its energy-momentum tensor?

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...
48. ### Energy-momentum tensor: metric tensor or kronecker tensor appearing?

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...
49. ### General Tensor contraction: Trace of Energy-Momentum Tensor (Einstein metric)

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...
50. ### I'm going crazy (Electromagnetic Energy-Momentum Tensor)

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...