Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region

Abstract

We suggest a method of construction of general diffeomorphism invariant boundary conditions for metric fluctuations. The case of $d+1$ dimensional Euclidean disk is studied in detail. The eigenvalue problem for the Laplace operator on metric perturbations is reduced to that on $d$-dimensional vector, tensor and scalar fields. Explicit form of the eigenfunctions of the Laplace operator is derived. We also study restrictions on boundary conditions which are imposed by hermiticity of the Laplace operator.

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• Lack of strong ellipticity in Euclidean quantum gravity
• Heat-Kernel Asymptotics with Generalized Boundary Conditions
• Consistent boundary conditions for supergravity
• The $a_{3/2}$ heat kernel coefficient for oblique boundary conditions
• Boundary Operators in Euclidean Quantum Gravity
• One-Loop Divergences in Simple Supergravity: Boundary Effects
• Heat Kernel Coefficients for Chern-Simons Boundary Conditions in QED
• Non-Local Boundary Conditions in Euclidean Quantum Gravity
• Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions
• One-Loop Effective Action for Euclidean Maxwell Theory on Manifolds with Boundary
• New Kernels in Quantum Gravity
• BRST-invariant boundary conditions and strong ellipticity
• Physics-to-gauge conversion at black hole horizons
• Essential self-adjointness in one-loop quantum cosmology
• Non-Local Properties in Euclidean Quantum Gravity
• Boundary Operators in Quantum Field Theory