The stress-energy-tensor tag has no wiki summary.
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Why is the stress-energy tensor symmetric?
The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$?
As a secondary question, how does this relate to the ...
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Why is the Maxwell Stress Tensor symmetric?
What is the physical meaning of the Maxwell Stress tensor symmetry?
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Have general relativistic effects of all of the components of the stress-energy tensor been measured?
The stress-energy tensor is:
Have general relativisic effects of all of the components of the stress-energy tensor been measured? I've heard that the accelerating expansion of the universe is due to ...
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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 ...
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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 ...
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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 ...
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Solving the equation of relativistic motion
How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
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1answer
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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 $(-, +, +, +)$ :
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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 ...
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1answer
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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 $E^2 = (pc)^2 + (mc^2)^2$ ...
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Perturbed stress-energy tensor in a cosmological context?
In the theory of cosmological pertubations, we can write the metric of a null-curvature expanding Universe as :
$ds^2 = -c^2\left(1+2\frac{\psi}{c^2}\right)dt^2 + a^2 ...
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Why is gravity such a unique force?
My knowledge on this particular field of physics is very sketchy, but I frequently hear of a theoretical "graviton", the quantum of the gravitational field. So I guess most physicists' assumption is ...
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Energy-momentum conservation without translation symmetry?
As I checked, the energy-momentum tensor defined as ${T^\mu}_\nu=\frac{\partial {\cal L}}{\partial(\partial_\mu \phi)}\partial_\nu \phi-{\cal L}{\delta^\mu}_\nu$ at the solution $\phi$ of equation of ...
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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 ...
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1answer
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What's the relativistic energy of a moving strained spring as $k\to\infty$ [closed]
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 ...
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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?
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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 ...
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Potential Energy in General Relativity
I often hear about how general relativity is very complicated because of all forms of energy are considered, including gravitation's own gravitational binding energy. I have two questions:
In ...
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Einstein tensor in Friedmann equations : where is the missing $c^2$?
I would like to demonstrate the several forms of the Friedmann equations WITH the $c^2$ factors. Everything is fine ... apart that I have a missing $c^2$ factor somewhere.
In all the following $\rho$ ...
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1answer
231 views
Geodesic Equation from energy-momentum conservation
I've been reading the excelent review from Eric Poisson found here.
While studying it I stumbled in a proof that I can't make... I can't find a way to go from Eq.(19.3) to the one before Eq.(19.4) ...
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1answer
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Flow of momentum is pressure
In the diagonal terms of the energy-momentum tensor, the flow of $x$-momentum in the $x$-direction is the $x$-pressure. Why the flow of momentum is pressure?
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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 ...
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Confused about indices of the Ricci tensor
In an intro to GR book the Ricci tensor is given as:
$$R_{\mu\nu}=\partial_{\lambda}\Gamma_{\mu \nu}^{\lambda}-\Gamma_{\lambda \sigma}^{\lambda}\Gamma_{\mu \nu}^{\sigma}-[\partial_{\nu}\Gamma_{\mu ...
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Having trouble seeing the similarity between these two energy-momentum tensors
Leonard Suskind gives the following formulation of the energy-momentum tensor in his Stanford lectures on GR (#10, I believe):
$$T_{\mu \nu}=\partial_{\mu}\phi \partial_{\nu}\phi-\frac{1}{2}g_{\mu ...
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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 ...
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4answers
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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). ...
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556 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 ...
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Finding the correct units for the energy-momentum tensor?
I'm trying to understand the energy-momentum tensor $T^{\mu\nu}$ but I'm confused about the units. My textbook says the components of $T^{\mu\nu}$ are $\mathrm{Jm^{-3}}$. Four-momentum is is given ...
5
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1answer
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Source term of the Einstein field equation
My copy of Feynman's "Six Not-So-Easy Pieces" has an interesting introduction by Roger Penrose. In that introduction (copyright 1997 according to the copyright page), Penrose complains that Feynman's ...
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1answer
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General parameters of the stress energy tensor in local inertial frame
A general 4x4 symmetric tensor has 10 independent components. How many components are we free to prescribe in the local inertial frame?
For example, relativistic dust is $\mbox{diag}(\rho c^2, 0, 0, ...
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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 ...
