Spectral Geometry of Nuts and Bolts
Abstract
We study the spectrum of Laplace operators on a one-parameter family of gravitational instantons of bi-axial Bianchi IX type coupled to an abelian connection with self-dual curvature. The family of geometries includes the Taub-NUT, Taub-bolt and Euclidean Schwarzschild geometries and interpolates between them. The interpolating geometries have conical singularities along a submanifold of co-dimension two, but we prove that the associated Laplace operators have natural self-adjoint extensions and study their spectra. In particular, we determine the essential spectrum and prove that its complement, the discrete spectrum, is infinite. We compute these eigenvalues numerically and compare the numerical results with an analytical approximation derived from the asymptotic Taub-NUT form of each of the geometries in our family.
Keywords
Cite
@article{arxiv.2112.11411,
title = {Spectral Geometry of Nuts and Bolts},
author = {Lyonell Boulton and Bernd Schroers and Kim Smedley-Williams},
journal= {arXiv preprint arXiv:2112.11411},
year = {2022}
}
Comments
27 pages, 2 figures and 3 tables; minor corrections throughout the text