A diffeomorphism-invariant eigenvalue problem for metric perturbations in a bounded region
Open Access
- 1 April 1996
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 13 (4) , 645-651
- https://doi.org/10.1088/0264-9381/13/4/006
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.Keywords
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This publication has 20 references indexed in Scilit:
- Mixed boundary conditions in Euclidean quantum gravityClassical and Quantum Gravity, 1995
- One-loop amplitudes in Euclidean quantum gravityPhysical Review D, 1995
- Gravitons in one-loop quantum cosmology: Correspondence between covariant and noncovariant formalismsPhysical Review D, 1994
- Conformal anomalies on Einstein spaces with boundaryPhysics Letters B, 1994
- Unitarity approach to quantum cosmologyPhysics Reports, 1993
- ONE-LOOP QUANTUM GRAVITY ON DE SITTER SPACEInternational Journal of Modern Physics A, 1993
- Mixed boundary conditions in quantum field theoryJournal of Mathematical Physics, 1991
- Boundary conditions for quantum cosmologyNuclear Physics B, 1990
- Quantum cosmology with antisymmetric tensor fieldsPhysics Letters B, 1990
- Semiclassical wave function of the Universe at small three-geometriesPhysical Review D, 1985