Exploring the Conformal Constraint Equations
摘要
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where the conformal factor vanishes, namely at the boundary representing null infinity. This problem can be avoided by means of a technique of H. Friedrich, which replaces the Einstein equations in the unphysical spacetime by an equivalent system of equations which is regular at the boundary. The initial value problem for these equations produces a system of constraint equations known as the conformal constraint equations. This work describes some of the properties of the conformal constraint equations and develops a perturbative method of generating solutions near flat space under certain simplifying assumptions.
引用
@article{arxiv.gr-qc/0111043,
title = {Exploring the Conformal Constraint Equations},
author = {Adrian Butscher},
journal= {arXiv preprint arXiv:gr-qc/0111043},
year = {2007}
}
备注
22 pages. Will appear in the proceedings of the internationl workshop on the conformal structure of spacetime (Tuebingen, Germany, April 2001). This is the final version and is significantly different from Version 1