Generalized Prices 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 $O(t^{-kappa-2+epsilon})$.