First-order action and Euclidean quantum gravity

Liko, Tomáš and Sloan, David (2009) First-order action and Euclidean quantum gravity. Classical and Quantum Gravity, 26 (14): 145004. ISSN 0264-9381

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.