Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region

Details Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region

1995-09-26

arxiv.org/abs/gr-qc/9509051v1

Class.Quant.Grav. 13 (1996) 645-652

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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Scientific paper

10.1088/0264-9381/13/4/006

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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