1992/05/11 by S. Carlip, Steven Carlip · 2 citations
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Effective action #Entropy (arrow of time) #Euclidean geometry #Geometry #Instanton #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Path integral formulation #Physics #Quantum #Quantum gravity #Quantum mechanics #Saddle #Saddle point #hep-th
paper · pdf · doi:10.1103/physrevd.46.4387
published as Phys.Rev.D46:4387-4395,1992 · 17 pages
arxiv created 1992/05/11 · openalex publication_date 1992/11/15 · arxiv updated 2010/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In most attempts to compute the Hartle-Hawking "wave function of the Universe" in Euclidean quantum gravity, two important approximations are made: the path integral is evaluated in a saddle-point approximation, and only the leading (least action) extremum is taken into account. In (2 + 1)-dimensional gravity with a negative cosmological constant, the second assumption is shown to lead to incorrect results: although the leading extremum gives the most important single contribution to the path integral, topologically inequivalent instantons with larger actions occur in great enough numbers to predominate. One can thus say that in 2 + 1 dimensions, and possibly in 3 + 1 dimensions as well, entropy dominates the action in the gravitational path integral.