Spectrum of the Laplacian on the Page metric

2024/12/27 by Robie A. Hennigar, Hennigar, Robie A., Hari K. Kunduri +5 · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry and complex manifolds #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2412.19879

openalex publication_date 2024/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We numerically construct the spectrum of the Laplacian on Page's inhomogeneous Einstein metric on \mathbbCP² # \mathbbCP² by reducing the problem to a (singular) Sturm-Liouville problem in one dimension. We perform a perturbative analysis based upon a closely related, exactly solvable problem that strongly supports our results. We also study the spectrum of the Lichnerowicz Laplacian on symmetric traceless transverse two-tensors. The method relies on both the isometries of the Page metric and pseudospectral methods to numerically solve the resulting ODEs.

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