Cosmological solutions of the Einstein-Friedmann equations ...

Cosmology
and the metric
ds 2 = 1 − Kr 2 (cdt) 2 −
1
1 − Kr 2 dr2 − r 2 dΩ 2
which is spherical symmetric with respect to any point and is regular. For K > 0
there is the de Sitter coordinate singularity K r 2 = 1. While for m 0 we have a
true singularity at r = 0, such a singularity is absent for m = 0.
Mappings
Λ > 0: de Sitter space dS 4
embedding into M 5 = R 1,4 : (cT) 2 − X 2 − Y 2 − Z 2 − W 2 = −a 2
ds 2 = (cdT) 2 − dX 2 + dY 2 + dZ 2 + dW 2
c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 483