Free decay of solutions to wave equations on a curved background
Free decay of solutions to wave equations on a curved background
We investigate for which metric g (close to the standard metric g 0 ) the solutions of the corresponding d’Alembertian behave like free solutions of the standard wave equation. We give rather weak (i.e., non integrable) decay conditions on g-g 0 ; in particular, g-g 0 decays like t -1 …