Maximal slicings in spherical symmetry: local existence and construction

Details Maximal slicings in spherical symmetry: local existence and construction Maximal slicings in spherical symmetry: local existence and construction

2011-11-11

arxiv.org/abs/1111.2717v1

J. Math. Phys. 52 (11) 112501 (2011)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, 6 figures

Scientific paper

10.1063/1.3658864

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.

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