- #1

TheMan112

- 43

- 1

A homogenous and isotropic hypersurface (disregarding time) has by definition the following line element (due to spherical symmetry):

[tex]d\sigma^2 = a^2 \left(\frac{1}{1-kr^2} dr^2 + r^2(d \theta^2 + sin^2(\theta) d \Phi^2) \right)[/tex]

Where k = -1, 0 or +1 and a is constant.

Why [tex]\frac{1}{1-kr^2} dr^2[/tex] ?

This is apparently very important as the value of k determines the evolution of the universe, but I don't know how to come to this line element.