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First-order action and Euclidean quantum gravity

Tomáš Liko1 and David Sloan

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We show that the on-shell path integral for asymptotically flat Euclidean spacetimes can be given in the first-order formulation of general relativity, without assuming the boundary to be isometrically embedded in Euclidean space and without adding infinite counter-terms. For illustrative examples of our approach, we evaluate the first-order action for the four-dimensional Euclidean Schwarzschild and NUT-charged spacetimes to derive the corresponding on-shell partition functions, and show that the correct thermodynamic quantities for the solutions are reproduced.


PACS

04.60.-m Quantum gravity

02.30.Rz Integral equations

MSC

83C45 Quantization of the gravitational field

81S40 Path integrals (See also 58D30)

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 14 (21 July 2009)

Received 27 October 2008, in final form 29 May 2009

Published 19 June 2009



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