Real Tunneling Solutions and the Hartle-Hawking Wave Function

Details Real Tunneling Solutions and the Hartle-Hawking Wave Function Real Tunneling Solutions and the Hartle-Hawking Wave Function

1993-01-08

arxiv.org/abs/gr-qc/9301006v1

Class.Quant.Grav.10:1057-1064,1993

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, LaTeX, UCD-92-30

Scientific paper

10.1088/0264-9381/10/6/004

A real tunneling solution is an instanton for the Hartle-Hawking path integral with vanishing extrinsic curvature (vanishing ``momentum'') at the boundary. Since the final momentum is fixed, its conjugate cannot be specified freely; consequently, such an instanton will contribute to the wave function at only one or a few isolated spatial geometries. I show that these geometries are the extrema of the Hartle-Hawking wave function in the semiclassical approximation, and provide some evidence that with a suitable choice of time parameter, these extrema are the maxima of the wave function at a fixed time.

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