https://doi.org/10.1140/epjc/s10052-022-10730-1
Regular Article - Theoretical Physics
Annihilation-to-nothing: DeWitt boundary condition inside a black hole
1
Department of Physics, McGill University, H3A 2T8, Montreal, QC, Canada
2
Institute of Physics, Academia Sinica, 11529, Taipei, Taiwan
3
Department of Physics Education, Pusan National University, 46241, Busan, Republic of Korea
4
Research Center for Dielectric and Advanced Matter Physics, Pusan National University, 46241, Busan, Republic of Korea
Received:
19
January
2022
Accepted:
18
August
2022
Published online:
1
September
2022
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.
© The Author(s) 2022
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