Maximal slicings in spherical symmetry: local existence and construction

TL;DR

This paper proves local existence of maximal slicings in spherically symmetric spacetimes, provides a geometric construction method, and demonstrates explicit examples in Minkowski and Friedmann universes, with applications in numerical relativity.

Contribution

It introduces a purely geometric procedure for constructing maximal slicings in spherically symmetric spacetimes, applicable to numerical relativity.

Findings

Maximal slicings exist locally in spherically symmetric spacetimes.

Explicit maximal foliations are constructed in Minkowski and Friedmann spacetimes.

The method is computationally efficient and adaptable for numerical relativity applications.

Abstract

We show that any spherically symmetric spacetime locally admits a maximal spacelike slicing and we give a procedure allowing its construction. The construction procedure that we have designed 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.