Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave Function

Details Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave Function Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave Function

1992-05-11

arxiv.org/abs/hep-th/9205022v1

Phys.Rev.D46:4387-4395,1992

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

10.1103/PhysRevD.46.4387

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 action in the gravitational path integral.

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