- #1
rubecuber
- 46
- 0
What is the Einstein-Vlaslov equation? Thanks !
- rubecuber
- rubecuber
EINSTEIN-VLASLOV EQUATION (to chriss HILMAN or anyone else who cares)
- Thread starter rubecuber
- Start date
- #2
Garth
Science Advisor
Gold Member
- 3,580
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Do you mean the http://www.emis.famaf.unc.edu.ar/journals/LRG/Articles/lrr-2002-7/node4.html equation?
It describes a self-gravitating collisionless gas.
Garth
It describes a self-gravitating collisionless gas.
Garth
Last edited by a moderator:
- #3
rubecuber
- 46
- 0
yes that one
please explain or give me it (if it is a single equation) (which i doubt)
thanks,
rubecuber
please explain or give me it (if it is a single equation) (which i doubt)
thanks,
rubecuber
- #4
cristo
Staff Emeritus
Science Advisor
- 8,144
- 75
rubecuber said:
Click on the link in Garth's post.
It's best to not normally address posts to one specific member, since they may not notice it, and it may discourage others from replying. Oh, and if you do address a post to one person; make sure you spell their name correctly!
I started reading a National Geographic article related to the Big Bang. It starts these statements:
Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits.
First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward.
My first reaction was that this is a layman's approximation to...
See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then
\begin{align}
0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\
&= \left(...
In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this:
$$
\partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}.
$$
The integrability conditions for the existence of a global solution ##F_{lj}## is:
$$
R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0
$$
Then from the equation:
$$\nabla_b e_a= \Gamma^c_{ab} e_c$$
Using cartesian basis ## e_I...
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