We study solutions of the decoupled Maxwell equations in the exterior region
of a Schwarzschild black hole. In stationary regions, where the Schwarzschild
coordinate r ranges over 2M<r1<r<r2, we obtain a decay rate of
t−1 for all components of the Maxwell field. We use vector field methods
and do not require a spherical harmonic decomposition.
In outgoing regions, where the Regge-Wheeler tortoise coordinate is large,
r∗>ϵt, we obtain decay for the null components with rates of
∣ϕ+∣∼∣α∣<Cr−5/2, ∣ϕ0∣∼∣ρ∣+∣σ∣<Cr−2∣t−r∗∣−1/2, and ∣ϕ−1∣∼∣α∣<Cr−1∣t−r∗∣−1. Along the event horizon and in ingoing regions, where r∗<0,
and when t+r∗1, all components (normalized with respect to an ingoing null
basis) decay at a rate of C \uout^{-1} with \uout=t+r_* in the exterior
region.Comment: 37 pages, 5 figure