Local energy decay for scalar fields on time dependent non-trapping backgrounds

Understand

We consider local energy decay estimates for solutions to scalar wave equations on nontrapping asymptotically flat space-times.

• Our goals are two-fold.
• First we consider the stationary case, where we can provide a full spectral characterization of local energy decay bounds; this characterization simplifies in the stationary symmetric case.
• Then we consider the almost stationary, almost symmetric case.