Quasimodes and a lower bound on the uniform energy decay rate for Kerr–AdS spacetimes
Quasimodes and a lower bound on the uniform energy decay rate for Kerr–AdS spacetimes
复制标题
准模态和 Kerr-AdS 时空均匀能量衰减率的下界
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Jacques Smulevici
中科院分区：
文献类型：
--
作者：
G. Holzegel;Jacques Smulevici
我们构造了Kerr-Anti-de Sitter（Kerr-AdS）时空黑洞外Klein-Gordon方程的准模.这种准模式与时间周期近似解的克莱因戈登方程，并提供了自然的候选人，以探测这些背景下的解决方案的衰减。它们被构造为分离变量后产生的半经典非线性本征值问题的解决方案，（逆）角动量扮演的半经典参数的作用。我们的建设结果在指数小误差的半经典参数。这意味着Kerr-AdS上的Klein Gordon方程的一般解不能比数学上更快地衰减。后一个结果完成了作者以前的工作，其中对数衰减率被确定为上限。
We construct quasimodes for the Klein-Gordon equation on the black hole exterior of Kerr-Anti-de Sitter (Kerr-AdS) spacetimes. Such quasi-modes are associated with time-periodic approximate solutions of the Klein Gordon equation and provide natural candidates to probe the decay of solutions on these backgrounds. They are constructed as the solutions of a semi-classical non-linear eigenvalue problem arising after separation of variables, with the (inverse of the) angular momentum playing the role of the semi-classical parameter. Our construction results in exponentially small errors in the semi-classical parameter. This implies that general solutions to the Klein Gordon equation on Kerr-AdS cannot decay faster than logarithmically. The latter result completes previous work by the authors, where a logarithmic decay rate was established as an upper bound.
影响因子：
4.9
作者：
Andersson, Lars;Blue, Pieter
通讯作者：
Blue, Pieter