In anti-De Sitter space, all world lines converge. In De Sitter space, all world lines diverge (due to expansion of space).

In a black hole all world lines converge (at the singularly), in a white hole won't all world lines diverge as they move away from the singularity? It would also explain why observers get individual pockets of horizons centered around themselves. You start at the center of this enormous white hole and travel towards outwards toward the edge everything near you spatialy becomes far from you spatially as the surface you are in spreads out.