Yes.
I don't know much of the physical meaning of them myself yet, but I'll try to explain what I know.
##\Theta_{r,0}## is the monopole radiation term.
##\Theta_{r,1}## is the dipole radiation term.
##\delta## is the dark matter density perturbation and ##v## is the bulk velocity...
I'm trying to numerically evolve the Einstein-Boltzmann equations for cold dark matter perturbations using Runge-Kutta method of the fourth order. There are 5 standard equations:
$$
\begin{align}
\dot{\Theta}_{r,0}+k\Theta_{r,1}&=-\dot{\Phi} \\
\dot{\Theta}_{r,1}+\frac{k}{3}\Theta_{r,0} &...
I don't understand how these 6 coefficients are equivalent in terms of making the metric Minkowski at a point.
Also, I couldn't understand how did you get the numbers? Can you please show the calculations for the number of coefficients and the number of first derivatives of the 10 components of...