Black Hole and de Sitter Microstructures from a Semiclassical Perspective

We describe two different, but equivalent semiclassical views of black hole physics in which the equivalence principle and unitarity are both accommodated. In one, unitarity is built-in, while the black hole interior emerges only effectively as a collective phenomenon involving horizon (and possibly other) degrees of freedom. In the other, more widely studied approach, the existence of the interior is manifest, while the unitarity of the underlying dynamics can be captured only indirectly by incorporating certain nonperturbative effects of gravity. These two pictures correspond to a distant description and the description based on entanglement islands/replica wormholes, respectively. We also present a holographic description of de Sitter spacetime based on the former approach, in which the holographic theory is located on the stretched horizon of a static patch. We argue that the existence of these two approaches is rooted in the two formulations of quantum mechanics: the canonical and path integral formalisms.