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

Abstract

We present an elementary physical space argument to establish local integrated decay estimates for the perturbed wave equation ${\square }_g\varphi =\epsilon {\beta }^a{\partial }_a\varphi$ on the exterior of the Schwarzschild geometry $(\mathcal{M},g)$. Here $\beta$ 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.

arXiv comment7 pages

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Cited by in corpus (1)

• Morawetz estimates without relative degeneration and exponential decay on Schwarzschild-de Sitter spacetimes