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

A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can evolve into a foliation of the $r>\mathrm{}3m/2\mathrm{}$ region of spacetime by maximal surfaces with the requirement that time run equally fast at both spatial ends of the manifold. This paper studies the behavior of these slices in the limit as proper time at infinity becomes arbitrarily large. It is shown that the central lapse decays exponentially and an analytic expression is given both for the exponent and for the preexponential factor.