Stress energy tensor Definition and 63 Threads

Hi, I would like to start from the stress energy tensor for the perfect fluid: T^{\mu\nu}=\begin{pmatrix} \rho c^2 & 0 & 0 & 0\cr 0 & p & 0 & 0\cr 0 & 0 & p & 0\cr 0 & 0 & 0 & p\cr\end{pmatrix} where \rho is the mass density and p is the pressure, and I would like to derive the...

This is page 96 in Wald's "General Relativity" He says that the stress energy tensor of the ordinary matter in the universe is of the form T_{ab}=\rho u_a u_b where \rho is the density of matter in the universe. why does it take this form? also are u_a and u_b orthogonal vectors in the...

Hi, I'm trying to compute P^{\mu} = \int d^{3}x T^{0\mu} where T is the stress energy tensor given by T^{\mu\nu} = \frac{\partial\mathcal{L}}{\partial[\partial_{\mu}\phi]}\partial^{\nu}\phi - g^{\mu\nu}\mathcal{L} for the scalar field \phi with the Lagrangian density given by \mathcal{L} =...

I'd appreciate any explanations of the physical interpretations of Einstein's stress energy tensor...for general relativity...maybe a favorite explanatory/expository online source. Wikipedia is not very satisfying on this nor on the electromagnetic stress energy tensor. For example all involve...

I've been trying to obtain the EM stress energy tensor... but I'm not sure if what I got is correct. In all the websites I googled, I found T^{\mu\nu} =- \frac{1}{4}g^{\mu\nu} F^{\alpha\beta}F_{\alpha\beta} + F^{\mu}\,\!_{\lambda}F^{\nu\lambda} However, is this with the sources or without...

This problem comes from the GR problem book, question 5.1 (b). The setup is a ring of N identical masses rotating in the x-y plane at a distance a from the origin. Assume that N is large enough so the ring may be treated as continuous. Ignore the stress energies keeping the particles in...

I don't see how in a static fluid the diagonal, space-like components of the stress-energy tensor are represented by pressure when every component of the stress-energy tensor is supposed to represent momentum in one direction or another. If a volume element of fluid is at rest (in my frame of...

What is a good intuitive way to think of the stress-energy tensor outside of Einstein's Ric-(1/2)Sg = 8pi T? I'm trying to understand the concept, but coming entirely from a math background I'm not quite getting it.

Hi, i need calculate the stress energy tensor for rotating 3D-disc in arbitrary rotation. where i can find some hint or perfomed calculations? thank you

is the stress energy tensor the same as the energy momentum tensor?

If I had a perfect fluid I could write the stress energy tensor in the rest frame of the fluid as a nice diagonal tensor with [rho,p,p,p] and use this to solve the field equations. Pressure is just random internal motions, so what happens if all the particles in my perfect fluid decide to...

In many textbooks on relativity, one finds at some point a statement that the vacuum stress energy tensor should be Lorentz invariant, from which it then follows that the vacuum pressure is minus the vacuum energy density. However, the vacuum energy density (or stress tensor) is not an...

Where can I found an expressionfor the shear stress tensor in GR with some explanation about it? Thanks blue