I am unclear about the calculation of $det(g_{ij})$ are there any tips or starting steps to reach this result?
I tried to rewrite $g_{ij}$ and I got:
$g_{ij}=a_{ij}(\rho+s(\rho_{0}s+\frac{3}{4}\rho_{1}))$, where $\rho,\rho_{0}$ and $\rho_{1}$ are the same as bellow.
I saw in a propozition that $det(g_{ij})$ can be calculated as: $det(g_{ij})=(1+\delta c^2) det (h_{ij})$, where $(h_{ij})$ is a symmetric matrix, and $c=\sqrt(h^{ij}c_i c_j)$. But I don't understand how it's supposed to be used. If someone has any advices, or can explain the first steps I need to make so I'll understand what I need to do, I will be grateful! I also searched in articles but unfortunately I didn't crossed with anything helpful.
