  We investigate the Schwarzschild-(anti) de Sitter spacetime with the
anisotropic metric ansatz. The Wheeler-DeWitt equation for such a metric is
solved numerically. In the presence of the cosmological constant $\Lambda$, we
show that two classical wave packets can be annihilated inside the black hole
horizon, i.e., the annihilation-to-nothing scenario. It is interesting that the
Wheeler-DeWitt equation can be extended to the asymptotic de Sitter spacetime
outside the cosmological horizon. Surprisingly, the only bounded nontrivial
wave function beyond the cosmological horizon satisfies the DeWitt boundary
condition, i.e., the wave function must vanish at a certain finite radius. This
might be an alternative explanation to the classicalization of quantum
fluctuations in the de Sitter space, where this topic is also related to
decoherence.
