A Vector Field Approach to Almost-Sharp Decay for the Wave Equation on Spherically Symmetric, Stationary Spacetimes

摘要: We present a new vector field approach to almost-sharp decay for the wave equation on spherically symmetric, stationary and asymptotically flat spacetimes. Specifically, we derive hierarchy of higher-order weighted energy estimates by employing appropriate commutator fields. In cases where an integrated local estimate holds, like in case sub-extremal Reissner–Nordstrom black holes, this leads global pointwise time-decay with rates that go beyond those obtained traditional method. Our play fundamental role our companion paper precise late-time asymptotics are linear scalar fields such backgrounds.