Generalized Price’s law on fractional-order asymptotically flat stationary spacetimes

We obtain estimates on the rate of decay of a solution to the wave equation on a stationary spacetime that tends to Minkowski space at a rate $O ({\lvert x \rvert}^{-\kappa}), \kappa \in (1,\infty) \backslash \mathbb{N}$. Given suitably smooth and decaying initial data, we show a wave locally enjoys the decay rate $O(t^{-\kappa-2+\epsilon})$.