From Osher Doctorow
My thread "The Raychaudhuri equation and expansion-contraction," April
14 through 17 on sci.physics, turns out to be relevant to the current
Rotation vs Expansion-Contraction thread, although I didn't spend much
time on rotation in the April thread.
I'm not moving away from Li's paper, but I've already referenced
Wlodzimierz Godlowski and Marek Szydlowski (Jagiellonian U., Poland)
"Dynamics of the universe with global rotation", astro-ph/0409073 v1 3
Sep 2004 on this thread, and let's take another look at what Godlowski
and Szydlowski say on page 3 of their paper: they reference Li's 1998
paper and their first equation is the Raychaudhuri equation which looks
so much like a (generalized) Riccati Differential equation in variable
y = (capital) theta where theta is the scalar expansion. We get:
1) d(theta)/dt = (1/3)theta^2 - 2(o^2 - w^2) + LAMBDA - 4piG(rho + 3p)
where w_ab is the rotation tensor, w^2 is its contraction divided by 2
w_ab w^ab/2, o_ab is the shear tensor, o^2 is (1/2) the contraction of
the latter, G is the gravitational constant, LAMBDA the cosmological
constant, rho the mass density, p its pressure, for a perfect fluid.
This is in section II of their paper, "Reduced Hamiltonian Dynamics of
FRW Universe With Global Rotation," (the section title), in which they
present the Hamiltonian dynamics of the FRW model with global rotation.
Osher Doctorow
.
|
