Conformal boundary ($\tilde{g}={\Omega }^{2}g,\Omega =0,d\Omega \ne 0$)

A boundary obtained by extending the rescaled metric $\tilde{g}={\Omega }^{2}g$ smoothly and nondegenerately to a hypersurface on which $\Omega$ vanishes with nonzero derivative. Its causal character is measured using the extended Lorentzian metric, not the divergent physical metric. In signature $(+---)$, a timelike normal makes the boundary spacelike, a spacelike normal makes it timelike, and a null normal makes it null. These cases lead to different causal and initial-value properties. The conformal cylinder of two-dimensional de Sitter spacetime has spacelike past/future boundaries; the conformal strip of two-dimensional anti-de Sitter spacetime has two timelike boundaries.