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First-order action and Euclidean quantum gravity

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Article number145004
<mark>Journal publication date</mark>06/2009
<mark>Journal</mark>Classical and Quantum Gravity
Issue number14
Number of pages8
Publication StatusPublished
<mark>Original language</mark>English


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.