Small-amplitude nonlinear waves on a black hole background (Q2571746)

Spherically symmetric solutions of \(\square _g\Phi =G(\Phi )\), where \(| G(x)| \leq K| x| ^p \) for \(| x| \leq C\), \(p>4\), \(g\) is Schwarzschild or Reissner-Nordström metrics, are considered. The authors proved, that solutions do not blow up in the domain of outer communications and decay in Eddington-Finkelstein advanced time and in static time, provided the initial data are small.