Decay estimates for waves on a black hole metric

黑洞度量上波的衰减估计

• 批准号: 0100406
• 负责人: Matei Machedon
• 金额: $ 13.5万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-06-01 至 2005-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100406&HistoricalAwards=false
• 关键词: Decay; estimates; waves; black; hole

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.

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。