A 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 the (d + 1)-dimensional Euclidean disc 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. The explicit form of the eigenfunctions of the Laplace operator is derived. We also study restrictions on boundary conditions which are imposed by the symmetry of the Laplace operator.
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