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.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- April 2012
- DOI:
- 10.1063/1.3702569
- arXiv:
- arXiv:1111.6019
- Bibcode:
- 2012JMP....53d2503B
- Keywords:
-
- 04.70.-s;
- 02.60.Lj;
- 04.20.-q;
- 04.20.Gz;
- Physics of black holes;
- Ordinary and partial differential equations;
- boundary value problems;
- Classical general relativity;
- Spacetime topology causal structure spinor structure;
- General Relativity and Quantum Cosmology;
- 83C15;
- 83C20;
- 83C57;
- 83C60
- E-Print:
- 10 pages