论文标题
在黑洞空位上的波动方程式上的注释，一阶小额订单术语
A note on the wave equation on black hole spacetimes with small non-decaying first order terms
论文作者
论文摘要
我们提出了一个基本的物理空间参数，以在schwarzschild几何$（\ Mathcal {m}，g）$上建立扰动的波动方程的局部集成衰减估计值$ \ box_g n = box_g n =εβ^a \ partial_a ϕ $。这里$β$是$ \ Mathcal {M} $在太空中适当衰减的常规vectorfield，但不一定是及时的。该证明是为了涵盖regge的扰动 - 轮毂方程。
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.
