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arXiv · 2412.19879

Spectrum of the Laplacian on the Page metric

Robie A. Hennigar·Hari K. Kunduri·Kam To Billy Sievers·Yiqing Wang
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Abstract

We numerically construct the spectrum of the Laplacian on Page's inhomogeneous Einstein metric on $\mathbb{CP}^2 \# \overline{\mathbb{CP}}^2$ 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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BibTeXRIS

Robie A. Hennigar, Hari K. Kunduri, Kam To Billy Sievers, Yiqing Wang. 2024-12-27. Spectrum of the Laplacian on the Page metric. https://arxiv.org/abs/2412.19879

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