Constructing "non-Kerrness" on compact domains

Bäckdahl, Thomas; Kroon, Juan A. Valiente

doi:10.1063/1.3702569

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Constructing "non-Kerrness" on compact domains

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Bäckdahl, Thomas
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1111.6019
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Citation

Bäckdahl, T., & Kroon, J. A. V. (2012). Constructing "non-Kerrness" on compact domains. Journal of Mathematical Physics, 53: 042503. doi:10.1063/1.3702569.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-5E21-1

Abstract

Given a compact domain of a 3-dimensional hypersurface on a vacuum spacetime, a scalar (the "non-Kerrness") is constructed by solving a Dirichlet problem for a second order elliptic system. If such scalar vanishes, and a set of conditions are satisfied at a point, then the domain of dependence of the compact domain is isometric to a portion of a member of the Kerr family of solutions to the Einstein field equations. This construction is expected to be of relevance in the analysis of numerical simulations of black hole spacetimes.