All Questions
11
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Degrees of freedom in stress-energy tensor
The stress-energy tensor has 16 components, but this question is only about the 9 components $T^{ij}$ with $i,j=1,2,3$. According to Wikipedia, these components are defined as follows:
The components ...
- 1,440
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Find the energy-impulse tensor of a fluid of charged dust from the action principle
I have the total action given by:
$$S_{tot} = -\frac{1}{16\pi c}\int d\Omega\ F^{\mu \nu}F_{\mu \nu} + \sum_{i=1}^{N}\bigg(-\frac{q}{c}\int dx_i^\mu A_\mu - mc \int ds_i\bigg) \\= \int d\Omega\ \frac{...
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Deriving relativistic equations of motion using scalar field stress-energy tensor
Question: Stress energy tensor of a minimally coupled scalar field is $T_{\mu\nu} = \partial_\mu\phi\partial_\nu\phi - \left[\frac{1}{2}(\nabla\phi)^2+V(\phi)\right]g_{\mu\nu}$.
Derive the scalar ...
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Special Relativity: Interpretation of the partial derivate of Stress-Energy Tensor
This question is based on Carroll's book Spacetime and Geometry, specifically from page 33 to page 36.
In the upper mentioned section we define the Stress-Energy Tensor as:
The flux of the four ...
- 4,577
2
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Momentum in capacitor field; How can an EM field have zero momentum density but non-zero momentum flux?
Consider the case of a simple, stationary parallel plate capacitor oriented with its plates lying in the x-y plane. The E-field is simply given by:
$$\vec{E} = \frac{Q}{\epsilon_0A}\hat{z} $$
with ...
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Lorentz transformation in spherical coordinates?
I am doing a practice problem (question 2006 in Lim,19951) which involves finding the flux of a star in an arbitrary inertial frame. given that it emits at luminosity $L$ at a frame at rest with ...
1
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2
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722
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What exactly is $T_{\mu\nu}$?
Continuous matter is described in special relativity by the matter tensor which is the so-called stress-energy-momentum tensor.
I am finding a difficulty understanding how a tensorial tool (...
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1
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672
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Tensors in special relativity [duplicate]
I'm trying to understand tensors, but I've come across the following question:
Let $T^{\mu\nu}$ by a $(2,0)$ tensor. Give the definitions of $T_\mu^{\,\nu}$, $T_{\mu\nu}$, and $T^{\mu}_{\,\nu}$. ...
- 633
2
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287
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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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1
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242
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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 ...
- 295
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544
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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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