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We investigate the Schwarzschild-(anti) de Sitter spacetime with theanisotropic metric ansatz. The Wheeler-DeWitt equation for such a metric issolved numerically. In the presence of the cosmological constant $\Lambda$, weshow that two classical wave packets can be annihilated inside the black holehorizon, i.e., the annihilation-to-nothing scenario. It is interesting that theWheeler-DeWitt equation can be extended to the asymptotic de Sitter spacetimeoutside the cosmological horizon. Surprisingly, the only bounded nontrivialwave function beyond the cosmological horizon satisfies the DeWitt boundarycondition, i.e., the wave function must vanish at a certain finite radius. Thismight be an alternative explanation to the classicalization of quantumfluctuations in the de Sitter space, where this topic is also related todecoherence.

Wheeler-DeWitt equation beyond the cosmological horizon: Annihilation to nothing, infinity avoidance, and loss of quantum coherence