The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms

Understand

We consider the perturbed covariant wave equation $\Box_{g_{M,a}} \Psi = \varepsilon \mathbf{B} \Psi$ on the exterior of a fixed subextremal Kerr spacetime $\left(\mathcal{M},g_{M,a}\right)$.

• Here $\mathbf{B}$ is a suitably regular first order differential operator respecting the symmetries of Kerr whose coefficients are assumed to decay in space but not in time.
• We establish integrated decay estimates for solutions of the associated Cauchy problem.
• The proof adapts the framework introduced by Dafermos--Rodnianski--Shlapentokh-Rothman \cite{DRSR} in the $\varepsilon=0$ case.