Abstract
The wave function of the Universe is usually taken to be a functional of the three-metric on a spacelike section, which is measured. It is sometimes better, however, to work in the conjugate representation, where the wave function depends on a quantity related to the second fundamental form of This makes it possible to ensure that is part of a Lorentzian universe by requiring that the argument of the wave function be purely imaginary. We demonstrate the advantages of this formalism first in the well-known examples of the nucleation of a de Sitter or a Nariai universe. We then use it to calculate the pair creation rate for sub-maximal black holes in de Sitter space, which had been thought to vanish semi-classically.
- Received 23 July 1998
DOI:https://doi.org/10.1103/PhysRevD.59.103501
©1999 American Physical Society
Erratum
Erratum: Lorentzian condition in quantum gravity [Phys. Rev. D 59, 103501 (1999)]
Raphael Bousso and Stephen Hawking
Phys. Rev. D 60, 109903 (1999)
Collections
This article appears in the following collection:
The Work of Stephen Hawking in Physical Review
To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters. They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."
