A note on the wave equation on black hole spacetimes with small non-decaying first order terms

We present an elementary physical space argument to establish local integrated decay estimates for the perturbed wave equation $\Box_g ϕ= εβ^a \partial_a ϕ$ on the exterior of the Schwarzschild geometry $(\mathcal{M},g)$. Here $β$ is a regular vectorfield on $\mathcal{M}$ decaying suitably in space but not necessarily in time. The proof is formulated to cover also perturbations of the Regge--Wheeler equation.

No reviews yet.

No comments yet.