Constructing "non-Kerrness" on compact domains

TL;DR

This paper introduces a method to construct a scalar measure called 'non-Kerrness' on compact domains in vacuum spacetimes, which helps identify regions that are isometric to Kerr black hole solutions, aiding numerical analysis.

Contribution

A novel elliptic system-based scalar is constructed to detect Kerr-like regions in vacuum spacetimes, with potential applications in numerical relativity.

Findings

Scalar vanishes for Kerr regions under certain conditions

Method distinguishes Kerr from non-Kerr spacetimes

Applicable to numerical simulations of black holes

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.