First-order action and Euclidean quantum gravity
arXiv:0810.0297 · doi:10.1088/0264-9381/26/14/145004
Abstract
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.
8 pages; v2: references added; minor corrections; v3: typos corrected in eqns (20) and (21); v4: substantially revised; addition of NUT-charged spacetimes; to appear in Classical and Quantum Gravity
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- Modifications in the Spectrum of Primordial Gravitational Waves Induced by Instantonic Fluctuations
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