Vacuum type D initial data
Abstract
A vacuum type D initial data set is a vacuum initial data set of the Einstein field equations whose data development contains a region where the spacetime is of Petrov type D. In this paper we give a systematic characterisation of a vacuum type D initial data set. By systematic we mean that the only quantities involved are those appearing in the vacuum constraints, namely the first fundamental form (Riemannian metric) and the second fundamental form. Our characterisation is a set of conditions consisting of the vacuum constraints and some additional differential equations for the first and second fundamental forms These conditions can be regarded as a system of partial differential equations on a Riemannian manifold and the solutions of the system contain all possible regular vacuum type D initial data sets. As an application we particularise our conditions for the case of vacuum data whose data development is a subset of the Kerr solution. This has applications in the formulation of the nonlinear stability problem of the Kerr black hole.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 September 2016
 DOI:
 10.1088/02649381/33/17/175005
 arXiv:
 arXiv:1602.08075
 Bibcode:
 2016CQGra..33q5005G
 Keywords:

 General Relativity and Quantum Cosmology;
 83C15;
 83C05
 EPrint:
 15 pages, no figures. Typos corrected and Theorem 7 on the characterization of the Kerr metric improved