Ill-posedness of a double null free evolution scheme for black hole   spacetimes
  We suggest that ``free evolution'' integration schemes for the Einstein equations (that do not enforce constraints) may contain exponentially growing modes that render them useless in numerical integrations of black hole spacetimes, independently of how the equations are differenced. As an example we consider the evolution of Schwarzschild and Reissner-Nordstr\"om spacetimes in double null coordinates. 
Carsten Gundlach and Jorge Pullin