The energy-momentum-tensor tag has no wiki summary.
19
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3answers
585 views
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 ...
10
votes
2answers
224 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 ...
5
votes
2answers
198 views
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 $\rho$ ...
5
votes
1answer
141 views
Confused about indices of the Ricci tensor
In an intro to GR book the Ricci tensor is given as:
$$R_{\mu\nu}=\partial_{\lambda}\Gamma_{\mu \nu}^{\lambda}-\Gamma_{\lambda \sigma}^{\lambda}\Gamma_{\mu \nu}^{\sigma}-[\partial_{\nu}\Gamma_{\mu ...
5
votes
1answer
114 views
Source term of the Einstein field equation
My copy of Feynman's "Six Not-So-Easy Pieces" has an interesting introduction by Roger Penrose. In that introduction (copyright 1997 according to the copyright page), Penrose complains that Feynman's ...
4
votes
1answer
120 views
Flow of momentum is pressure
In the diagonal terms of the energy-momentum tensor, the flow of $x$-momentum in the $x$-direction is the $x$-pressure. Why the flow of momentum is pressure?
4
votes
1answer
213 views
Geodesic Equation from energy-momentum conservation
I've been reading the excelent review from Eric Poisson found here.
While studying it I stumbled in a proof that I can't make... I can't find a way to go from Eq.(19.3) to the one before Eq.(19.4) ...
3
votes
3answers
136 views
Having trouble seeing the similarity between these two energy-momentum tensors
Leonard Suskind gives the following formulation of the energy-momentum tensor in his Stanford lectures on GR (#10, I believe):
$$T_{\mu \nu}=\partial_{\mu}\phi \partial_{\nu}\phi-\frac{1}{2}g_{\mu ...
3
votes
1answer
69 views
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, ...
3
votes
0answers
142 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 ...
2
votes
1answer
68 views
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 ...
2
votes
1answer
224 views
Double gyroscope: Can a spinning pencil tumble on only one axis?
Picture an object such as item 7 on this page .. http://en.wikipedia.org/wiki/List_of_moment_of_inertia_tensors
Call that the x axis and z is in to the distance. See diagram below.
We are in deep ...
1
vote
2answers
139 views
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 ...
1
vote
1answer
178 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?
1
vote
1answer
229 views
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 ...
1
vote
1answer
161 views
Show that $\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$
In a theoretical physics homework problem, I have to show the following:
$$\partial_\nu T^{\mu\nu} = - j_\nu F^{\mu\nu}$$
Where $T$ is the Energie-Momentum-Tensor, $j$ the generalized current and $F$ ...
1
vote
0answers
42 views
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 ...
0
votes
0answers
23 views
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 ...
