On the local existence of maximal slicings in spherically symmetric spacetimes

TL;DR

This paper proves that any spherically symmetric spacetime can locally be sliced into maximal spacelike hypersurfaces, providing a systematic method to construct such slicings either analytically or numerically.

Contribution

It establishes the local existence of maximal slicings in spherically symmetric spacetimes and offers a general procedure for their construction.

Findings

Maximal slicings exist locally in all spherically symmetric spacetimes.

A decoupled system of PDEs characterizes the maximal slicing condition.

The method can be implemented analytically or numerically.

Abstract

In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.