A decay estimate for a wave equation with trapping and a complex   potential
  In this brief note, we consider a wave equation that has both trapping and a complex potential. For this problem, we prove a uniform bound on the energy and a Morawetz (or integrated local energy decay) estimate. The equation is a model problem for certain scalar equations appearing in the Maxwell and linearised Einstein systems on the exterior of a rotating black hole. 
Lars Andersson, Pieter Blue, Jean-Philippe Nicolas
math.AP gr-qc