Constructing "non-Kerrness" on compact domains

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.

10 pages

References in corpus (4)

• Geometric Invariant Measuring the Deviation from Kerr Data
• On the construction of a geometric invariant measuring the deviation from Kerr data
• The "non-Kerrness" of domains of outer communication of black holes and exteriors of stars
• Approximate twistors and positive mass

Cited by in corpus (9)

• On choosing the start time of binary black hole ringdown
• Schwarzschild and Kerr Solutions of Einstein's Field Equation -- an introduction
• Spin geometry and conservation laws in the Kerr spacetime
• A local non-negative initial data scalar characterisation of the Kerr solution
• A set of invariant quality factors measuring the deviation from the Kerr metric
• Killing spinors as a characterisation of rotating black hole spacetimes
• Closed conformal Killing-Yano initial data
• A geometric invariant characterising initial data for the Kerr-Newman spacetime
• Perturbations of Kerr with approximate Killing spinors -- Wave version