A DIFFEOMORPHISM-INVARIANT EIGENVALUE PROBLEM FOR METRIC PERTURBATIONS IN A BOUNDED REGION

We suggest a method of construction of general diffeomorphism-invarian t boundary conditions for metric fluctuations. The case of the (d + 1) -dimensional Euclidean disc is studied in detail. The eigenvalue probl em 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 stud y restrictions on boundary conditions which are imposed by the symmetr y of the Laplace operator.