First-order action and Euclidean quantum gravity
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.
Cite
@article{arxiv.0810.0297,
title = {First-order action and Euclidean quantum gravity},
author = {Tomas Liko and David Sloan},
journal= {arXiv preprint arXiv:0810.0297},
year = {2009}
}
Comments
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