Spectral geometry of nuts and bolts

Lyonell Boulton, Bernd J. Schroers*, Kim Smedley-Williams

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
25 Downloads (Pure)


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 (TN), 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 selfadjoint extensions and study their spectra. In particular, we determine the essential spectrum and prove that its complement, the discrete spectrum, is infinite. We compute some of these eigenvalues numerically and compare the numerical results with an analytical approximation derived from the asymptotic TN form of each of the geometries in our family.

Original languageEnglish
Article number235202
JournalJournal of Physics A: Mathematical and Theoretical
Issue number23
Early online date20 May 2022
Publication statusPublished - 10 Jun 2022


  • Euclidean Schwarzschild space
  • gravitational instanton
  • Laplace operator
  • nuts and bolts
  • spectrum
  • Taub-bolt space
  • Taub-NUT space

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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