Gravitational Instantons, Confocal Quadrics and Separability of the Schrödinger and Hamilton-Jacobi equations

Abstract

A hyperkähler 4-metric with a triholomorphic SU(2) action gives rise to a family of confocal quadrics in Euclidean 3-space when cast in the canonical form of a hyperkähler 4-metric metric with a triholomorphic circle action. Moreover, at least in the case of geodesics orthogonal to the U(1) fibres, both the covariant Schrödinger and the Hamilton-Jacobi equation is separable and the system integrable.

arXiv comment10 pages Latex

References in corpus (4)

• HyperKähler Quotient Construction of BPS Monopole Moduli Spaces
• Harmonic functions, central quadrics, and twistor theory
• Gravitational Instantons from Minimal Surfaces
• The eigenvalue equation on the Eguchi-Hanson space

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• Tachyonization of the $\La$CDM cosmological model
• Gauge invariant description of weak gravitational field on a spherically symmetric background with cosmological constant
• The geodesic flow of the BGPP metric is Liouville integrable