Late time behaviour of the maximal slicing of the Schwarzschild black hole

TL;DR

This paper analyzes the late-time behavior of maximal slices in Schwarzschild spacetime, providing an analytic expression for the lapse collapse as proper time at infinity grows large.

Contribution

It offers an analytic description of the collapse of maximal slicing in Schwarzschild black holes at late times, extending understanding of spacetime foliation behavior.

Findings

Derived an explicit formula for lapse collapse at late times

Characterized the asymptotic approach of slices to the event horizon

Enhanced understanding of black hole spacetime foliation dynamics

Abstract

A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be evolved into a foliation of the $r>3m/2$-region of the spacetime by maximal surfaces with the requirement that time runs equally fast at both spatial ends of the manifold. This paper studies the behaviour of these slices in the limit as proper time-at-infinity becomes arbitrarily large and gives an analytic expression for the collapse of the lapse.