A1 Journal article (refereed)
Spherically Symmetric Terrestrial Planets with Discontinuities Are Spectrally Rigid (2024)
Ilmavirta, J., de Hoop, M. V., & Katsnelson, V. (2024). Spherically Symmetric Terrestrial Planets with Discontinuities Are Spectrally Rigid. Communications in Mathematical Physics, 405(2), Article 31. https://doi.org/10.1007/s00220-023-04892-6
JYU authors or editors
Publication details
All authors or editors: Ilmavirta, Joonas; de Hoop, Maarten V.; Katsnelson, Vitaly
Journal or series: Communications in Mathematical Physics
ISSN: 0010-3616
eISSN: 1432-0916
Publication year: 2024
Publication date: 01/02/2024
Volume: 405
Issue number: 2
Article number: 31
Publisher: Springer
Publication country: Germany
Publication language: English
DOI: https://doi.org/10.1007/s00220-023-04892-6
Publication open access: Not open
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/93372
Publication is parallel published: https://arxiv.org/abs/2302.14158
Abstract
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in between the interfaces enabling the consideration of two wave types, like P- and S-polarized waves in isotropic elastic solids. Terrestrial planets in our solar system are approximately spherically symmetric and support toroidal and spheroidal modes. Discontinuities typically correspond with phase transitions in their interiors. Our rigidity result applies to such planets as we ensure that our conditions are satisfied in generally accepted models in the presence of a fluid outer core. The proof is based on a novel trace formula. We also prove that the length spectrum of the Euclidean ball is simple.
Keywords: differential geometry; partial differential equations; manifolds (mathematics); inverse problems; planets; mathematical models
Contributing organizations
Ministry reporting: Yes
VIRTA submission year: 2024
Preliminary JUFO rating: 3
