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

TL;DR

This paper explores quantum behavior in Schwarzschild-(anti) de Sitter spacetime using the Wheeler-DeWitt equation, revealing phenomena like wave packet annihilation inside horizons and unique boundary conditions outside the cosmological horizon, impacting quantum cosmology.

Contribution

It extends the Wheeler-DeWitt equation analysis beyond the cosmological horizon and uncovers novel boundary conditions and annihilation scenarios in quantum black hole and de Sitter spacetimes.

Findings

Wave packets can annihilate inside black hole horizons.

The wave function outside the cosmological horizon must vanish at a finite radius.

A bounded nontrivial wave function satisfies the DeWitt boundary condition.

Abstract

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.