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arXiv · 2111.02337

Quasi-isometric embedding of Kerr poloidal sub-manifolds

L. Chantry·F. Dauvergne·Y. Temmam·V. Cayatte
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Abstract

We propose two approaches to obtain an isometric embedding of the poloidal Kerr sub-manifold. The first one relies on the convex integration process using the corrugation from a primitive embedding. This allows us to obtain one parameter family of embeddings reaching the limits of an isometric embedding. The second one consists in consecutive numerical resolutions of the Gauss-Codazzi-Mainardi and frame equations. This method requires geometric assumptions near the equatorial axis of the poloidal sub-manifold to get initial and boundary conditions. The second approach allows to understand some physical properties in the vicinity of a Kerr black hole, in particular the fast increasing ergoregion extent with angular momentum.

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L. Chantry, F. Dauvergne, Y. Temmam, V. Cayatte. 2021-11-03. Quasi-isometric embedding of Kerr poloidal sub-manifolds. https://doi.org/10.1088/1361-6382%2Fac08a6

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