Abstract
We consider the asymptotics of a Maxwell field in Schwarzschild and Kerr spacetimes. In a Kerr spacetime, we utilize the basic energy and Morawetz estimates proven in earlier work to derive pointwise estimates where the total power of decay rate for all components of the Maxwell field towards a stationary solution is −7/2. Moreover, on a Schwarzschild background, if the constructed Newman–Penrose constant vanishes (or does not vanish), we prove almost sharp Price's law decay v−2−sτ−3+s+ (or v−2−sτ−2+s+) for Maxwell field and v−2−sτ−2+s−ℓ0+ (or v−2−sτ−1+s−ℓ0+) for the ℓ≥ℓ0 modes of the field towards a static solution, with s being the spin weight of the Newman–Penrose components of Maxwell field. All estimates are uniform in the exterior of the black hole.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have