Maximal slicings in spherical symmetry: Local existence and construction

Abstract

We show that any spherically symmetric spacetime locally admits a maximal space-like slicing and we give a procedure allowing its construction. The designed construction procedure is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first-order quasi-linear partial differential equations. We have explicitly built up maximal foliations in Minkowski and Friedmann spacetimes. Our approach admits further generalizations and efficient computational implementation. As by-product, we suggest some applications of our work in the task of calibrating numerical relativity complex codes, usually written in Cartesian coordinates.