The stress-energy-tensor tag has no wiki summary.
4
votes
0answers
41 views
Symmetry of the stress tensor
When presenting the stress tensor (say in a non-relativistic context), it is shown to be a tensor in the sense that it is a linear vector transformation: it operates on a vector $n$ (the normal to a ...
0
votes
1answer
42 views
Does the actual curvature of spacetime hold energy?
My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy ...
3
votes
2answers
119 views
Probability Density Function for Dust in the Colision-less Vlasov equation
My problem is the following: I'm trying to model a dust (pressure-less relativistic gas) in the presence of electromagnetic field using colisioness vlasov-equation (relativistic version of boltzmann ...
2
votes
1answer
85 views
Stress energy tensor of a perfect fluid and four-velocity
In the following demonstration, there is an error, but I cannot find where. (I explicitely put the $c^2$ to keep track of units).
We consider a metric $g_{\mu\nu}$ with a signature $(-, +, +, +)$ :
...
3
votes
3answers
85 views
Why is the (nonrelativistic) stress tensor linear and symmetric?
From wikipedia:
"...the stress vector $T$ across a surface will always be a linear function of the surface's normal vector $n$, the unit-length vector that is perpendicular to it.
...The linear ...
1
vote
1answer
50 views
Does non-mass-energy generate a gravitational field?
At a very basic level I know that gravity isn't generated by mass but rather the stress-energy tensor and when I wave my hands a lot it seems like that implies that energy in $E^2 = (pc)^2 + (mc^2)^2$ ...
0
votes
1answer
75 views
Tensor manipulation
Having a bit of trouble applying what I know about tensor manipulation, given,
$T^{\mu \nu} = \left( g^{\mu \nu} - \frac{p^\mu n^\nu + p^\nu n^\mu}{p \cdot n} \right)$,
I need to compute quantities ...
0
votes
1answer
72 views
What's the relativistic energy of a moving strained spring as $k\to\infty$
Suppose a spring with stiffness $k$, is strained by constant forces on each end.
In a frame where the strained spring moves at a constant velocity, what's the total relativistic energy of the moving ...
1
vote
1answer
174 views
Scalar field stress energy tensor
Can anyone explain why $T_{\mu \nu} = \frac{2}{\sqrt{-g}} \frac{\delta \mathcal{L}_M}{\delta g^{\mu \nu}} $, other than justifying it from the einstein field equations?
2
votes
1answer
92 views
Showing symmetry of the stress tensor by applying divergence theorem to $\int\int_{\delta V(t)} \vec{x}\times \vec{t} dS$
I'm currently working through the symmetry of the stress tensor, in relation to viscous flow. I am looking at this by examining the conservation of angular momentum equation for a material volume ...
3
votes
0answers
141 views
Symmetrizing the Canonical Energy-Momentum Tensor
The Canonical energy momentum tensor is given by
$$T_{\mu\nu} = \frac{\delta {\cal L}}{\delta (\partial^\mu \phi_s)} \partial_\nu \phi_s - g_{\mu\nu} {\cal L} $$
A priori, there is no reason to ...
3
votes
3answers
136 views
Having trouble seeing the similarity between these two energy-momentum tensors
Leonard Suskind gives the following formulation of the energy-momentum tensor in his Stanford lectures on GR (#10, I believe):
$$T_{\mu \nu}=\partial_{\mu}\phi \partial_{\nu}\phi-\frac{1}{2}g_{\mu ...
1
vote
2answers
219 views
fourth rank tensor for stress energy
The Weyl tensor equates the Riemann tensor in vacuum
$$ C_{\mu \nu \eta \lambda} = R_{\mu \nu \eta \lambda} $$
So it makes me wonder about the tensor
$$T_{\mu \nu \eta \lambda} = C_{\mu \nu \eta ...
3
votes
4answers
210 views
Formulation of general relativity
EDIT: I think I can pinpoint my confusion a bit better. Here comes my updated question (I'm not sure what the standard way of doing things is - please let me know if I should delete the old version). ...
6
votes
1answer
520 views
What is the stress energy tensor?
I'm trying to understand the Einstein Field equation equipped only with training in Riemannian geometry. My question is very simple although I cant extract the answer from the wikipedia page:
Is the ...
10
votes
2answers
223 views
The derivation of the Belinfante-Rosenfeld tensor
It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the ...
