Maximal slicing for puncture evolutions of Schwarzschild and Reissner-Nordstrom black holes -: art. no. 044006

We prove by explicit construction that there exists a maximal slicing of the Schwarzschild spacetime such that the lapse has zero gradient at the puncture. This boundary condition has been observed to hold in numerical evolutions, but in the past it was not clear whether the numerically obtained maximal slices exist analytically. We show that our analytical result agrees with numerical simulation. Given the analytical form for the lapse, we can derive that at late times the value of the lapse at the event horizon approaches the value 3/16root3approximate to0.3248, justifying the numerical estimate of 0.3 that has been used for black hole excision in numerical simulations. We present our results for the nonextremal Reissner-Nordstrom metric, generalizing previous constructions of maximal slices.