Spectral geometry of nuts and bolts
Spectral geometry of nuts and bolts
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DOI：
10.1088/1751-8121/ac6996
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发表时间：
2022-06-10
影响因子：
2.1
通讯作者：
Smedley-Williams, Kim
中科院分区：
文献类型：
--
作者：
Boulton, Lyonell;Schroers, Bernd J.;Smedley-Williams, Kim
研究了耦合到具有自对偶曲率的阿贝尔联络的双轴比安奇IX型单参数引力瞬子族上的拉普拉斯算子的谱.几何家族包括陶布-NUT（TN）、陶布-博尔特和欧几里得史瓦西几何，以及它们之间的插值。内插几何有锥形奇点沿着的余维2的子流形，但我们证明了相关的拉普拉斯运营商有自然的自伴扩张，并研究其频谱。特别是，我们确定的本质谱，并证明其补充，离散谱，是无限的。我们计算这些特征值的数值和比较的数值结果与来自我们的家庭中的每个几何形状的渐近TN形式的解析近似。
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.