Decay estimates for waves on a black hole metric

在与Sergiu Klainerman和John Stalker的联合工作中，我们研究了Schwarzschild背景度规上线性波动方程解的逐点和均匀衰减率。我们对每个球谐函数都有了初步的结果。这是理解这些度规的非线性稳定性的第一步。粗略地说，这对应于黑洞附近电磁波的传播和衰减。我们的工作从对物理学家已知的想法进行仔细的数学分析开始，并计划开发新的工具。

In joint work with Sergiu Klainerman and John Stalker,we study the decay rate, pointwise and uniform, of solutionsto a linear wave equation on a Schwarzschild background metric.We have preliminary results for each spherical harmonic.This is the first step towards understanding the non-linear stabilityof these metrics.Roughly speaking, this corresponds to the propagation and decay of anelectromagnetic wave near a black hole. Our work starts with a carefulmathematical analysis of ideas known to physicists, and plans todevelop new tools.