Parametric Equation of a Sphere in General relativity

[Reedeegi]

What parametric equation would one use to describe a sphere in General Relativity in order to calculate curvature? My main problem is what to do with the time dimension... And no, this is not a homework question.

 

[atyy]

Eq 1, Burko et al, http://arxiv.org/abs/gr-qc/0008065
Eq 3.9, 3.10, 4.1, 4.7, Ehlers et al, http://arxiv.org/abs/gr-qc/0510041