How Slice Stretching arises when Maximally Slicing the Schwarzschild Spacetime with Vanishing Shift

When foliating the extended Schwarzschild spacetime with maximal slices while using zero shift, slice stretching effects such as slice sucking and slice wrapping arise. These effects are due to the differential infall of Eulerian observers and can be quantified for arbitrary spatial coordinates in the context of even boundary conditions. As examples logarithmic and isotropic grid coordinates are discussed. For boundary conditions where the lapse arises as a linear combination of odd and even lapse, two integrals are introduced which characterize the overall slice stretching. Favorable boundary conditions are then derived which make slice stretching occur late in numerical simulations. Allowing the lapse to become negative, this requirement leads to lapse functions which approach at late times the odd lapse corresponding to the static Schwarzschild metric. Demanding in addition that a numerically favorable lapse remains non-negative, as result the average of odd and even lapse is obtained. At late times the lapse with zero gradient at the puncture arising for the puncture evolution is precisely of this form. Finally a one-parameter family of boundary conditions is studied numerically and agreement with analytical results is found.