First-order action and Euclidean quantum gravity

Details First-order action and Euclidean quantum gravity First-order action and Euclidean quantum gravity

2008-10-02

arxiv.org/abs/0810.0297v4

Class.Quant.Grav.26:145004,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages; v2: references added; minor corrections; v3: typos corrected in eqns (20) and (21); v4: substantially revised; additi

Scientific paper

10.1088/0264-9381/26/14/145004

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.

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