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arXiv · 2403.05475

Geometric inverse problems on gas giants

Maarten V. de Hoop·Joonas Ilmavirta·Antti Kykkänen·Rafe Mazzeo
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Abstract

On gas giant planets the speed of sound is isotropic and goes to zero at the surface. Geometrically, this corresponds to a Riemannian manifold whose metric tensor has a conformal blow-up near the boundary. The blow-up is tamer than in asymptotically hyperbolic geometry: the boundary is at a finite distance. We study the differential geometry of such manifolds, especially the asymptotic behavior of geodesics near the boundary. We relate the geometry to the propagation of singularities of a hydrodynamic PDE and we give the basic properties of the Laplace--Beltrami operator. We solve two inverse problems, showing that the interior structure of a gas giant is uniquely determined by different types of boundary data.

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Maarten V. de Hoop, Joonas Ilmavirta, Antti Kykkänen, Rafe Mazzeo. 2024-03-08. Geometric inverse problems on gas giants. https://arxiv.org/abs/2403.05475

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