The eigenvalue equation on the Eguchi-Hanson space

Abstract

We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation with Ince symbol [0,2,1_2]. We construct approximations for the eigenfunctions and their asymptotic scattering phases with the help of the Liouville-Green approximation (WKB). Furthermore, for specific discrete eigenvalues obtained by a continued T-fraction we construct the solution by the Frobenius method and determine its scattering phase by a monodromy computation.

29 pages, 32 figures

References in corpus (1)

• Collapsing D-Branes in Calabi-Yau Moduli Space: I

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• Bounding the Heat Trace of a Calabi-Yau Manifold
• Exact Solutions to Einstein-Maxwell theory on Eguchi-Hanson Space
• On Certain Solutions for Confluent and Double-Confluent Heun Equations
• A limit of the confluent Heun equation and the Schroedinger equation for an inverted potential and for an electric dipole