Uniform energy bound and asymptotics for the Maxwell field on a slowly rotating Kerr black hole exterior

Understand

We consider the Maxwell equation in the exterior of a very slowly rotating Kerr black hole.

• For this system, we prove the boundedness of a positive definite energy on each hypersurface of constant $t$.
• We also prove the convergence of each solution to a stationary Coulomb solution.
• We separate a general solution into the charged, Coulomb part and the uncharged part.