Annihilation-to-nothing: DeWitt boundary condition inside a black hole

TL;DR

This paper explores the DeWitt boundary condition inside black holes, proposing that the wave function vanishes at the singularity due to destructive interference and symmetry, with implications for loop quantum gravity and the nature of black hole interiors.

Contribution

It generalizes the DeWitt boundary condition, interprets it through symmetry and interference, and connects it to loop quantum gravity models with a new perspective on time arrows.

Findings

Wave function vanishes near the singularity due to destructive interference.

Symmetry between black hole and anti-black hole geometries leads to annihilation.

Loop quantum gravity models support the symmetric annihilation interpretation.

Abstract

In canonical quantum gravity, the wave function for a hypersurface inside a Schwarzschild black hole can be obtained by solving the Wheeler-DeWitt equation. What is of prime importance is the behavior of the wave function for the future boundary near the singularity, and the DeWitt boundary condition implies that it should vanish here. In this paper, we provide several generalizations, and new interpretations, of the DeWitt boundary condition. First, we summarize existing works on the wave function inside the black hole to justify the DeWitt boundary condition. Next, we investigate the wave function for the collapsing null shell to show that due to the reflection symmetry in space and time, there exists a destructive interference near the singularity and hence a vanishing boundary condition can be natural. If we extend this point of view to the black hole spacetime itself, then the DeWitt boundary condition is equivalent to saying that there exists a symmetric anti-black hole contribution, such that eventually these two geometries are annihilated-to-nothing near the quantum transition surface. This symmetric model can be realized within black hole models of loop quantum gravity with a novel interpretation for the arrow(s) of time.