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arXiv 2005.13644gr-qcmath.AP
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具有小的非衰减一阶项的黑洞时空波动方程的注记

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

Gustav Holzegel, Christopher Kauffman

摘要:

我们提出了一个基本的物理空间参数建立局部集成的衰变估计的扰动波动方程$\Box_g ϕ= εβ^a \partial_a ϕ$的外部Schwarzschild几何$(\mathcal{M},g)$。这里$β$是$\mathcal{M}$上的规则向量场,在空间上适当地衰减,但不一定在时间上衰减。证明制定覆盖也扰动的Regge-Wheeler方程。

英文摘要:

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.

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