Two-boundary problems in Euclidean quantum gravity

TL;DR

This paper investigates two-boundary problems in Euclidean quantum gravity, applying Robin and Dirichlet boundary conditions to compute one-loop divergences on a bounded flat space segment.

Contribution

It introduces a novel application of mixed boundary conditions to evaluate quantum gravitational divergences in a bounded Euclidean space.

Findings

Computed one-loop divergences with new boundary conditions

Demonstrated the impact of boundary conditions on quantum gravity calculations

Provided insights into boundary effects in Euclidean quantum gravity

Abstract

Recent work in the literature has studied a new set of local boundary conditions for the quantized gravitational field, where the spatial components of metric perturbations, and ghost modes, are subject to Robin boundary conditions, whereas normal components of metric perturbations obey Dirichlet boundary conditions. Such boundary conditions are here applied to evaluate the one-loop divergence on a portion of flat Euclidean four-space bounded by two concentric three-spheres.