Conformal completion
= Conformal completion
{wiki=Conformal_compactification}
A conformal completion embeds a physical spacetime $(\mathcal M,g)$ into a manifold with boundary carrying a regular metric $\bar g=\Omega^2g$. Infinity is represented by $\Omega=0$ with $d\Omega\ne0$; the causal character of each boundary component is determined by $\bar g^{ab}\bar\nabla_a\Omega\bar\nabla_b\Omega$.