1993/01/08 by S. Carlip, S Carlip · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Curvature #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Instanton #Maxima and minima #Momentum (technical analysis) #Quantum tunnelling #Wave function #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/10/6/004
published as Class.Quant.Grav.10:1057-1064,1993 · 10 pages, LaTeX, UCD-92-30
arxiv created 1993/01/08 · openalex publication_date 1993/06/01 · arxiv updated 2010/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A real tunnelling 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 specific freely; consequently, such an instanton will contribute to the wavefunction at only one or a few isolated spatial geometries. The author shows that these geometries are the extrema of the Hartle-Hawking wavefunction in the semiclassical approximation, and provide some evidence that with a suitable choice of time parameter, these extrema are the maxima of the wavefunction at a fixed time.