Wormholes and trumpets: the Schwarzschild spacetime for the   moving-puncture generation
  We expand upon our previous analysis of numerical moving-puncture simulations of the Schwarzschild spacetime. We present a derivation of the family of analytic stationary 1+log foliations of the Schwarzschild solution, and outline a transformation to isotropic-like coordinates. We discuss in detail the numerical evolution of standard Schwarzschild puncture data, and the new time-independent 1+log data. Finally, we demonstrate that the moving-puncture method can locate the appropriate stationary geometry in a robust manner when a numerical code alternates between two forms of 1+log slicing during a simulation. 
Mark Hannam, Sascha Husa, Frank Ohme, Bernd Bruegmann, Niall   O'Murchadha