Kerr 与 Kerr-de Sitter 时空中拟正规模的解析性

A global definition of quasinormal modes for Kerr-AdS Black Holes

The quasinormal frequencies of massive scalar fields on Kerr-AdS black holes are identified with poles of a certain meromorphic family of operators, once boundary conditions are specified at the conformal boundary. Consequently, the quasinormal frequencies form a discrete subset of the complex plane and the corresponding poles are of finite rank. This result holds for a broad class of elliptic boundary conditions, with no restrictions on the rotation speed of the black hole.

Existence of quasinormal modes for Kerr-AdS black holes

This paper establishes the existence of quasinormal frequencies converging exponentially to the real axis for the Klein--Gordon equation on a Kerr-AdS spacetime when Dirichlet boundary conditions are imposed at the conformal boundary. The proof is adapted from results in Euclidean scattering about the existence of scattering poles generated by time-periodic approximate solutions to the wave equation.

Kerr黑洞的准正规模式

Quasinormal modes for the Kerr black hole

本文通过结合复标度与微局部分析方法，严格定义Kerr黑洞的准正规模式，并证明其高能谱隙存在且不会在零能量处累积。

Kerr时空上的准正规模式

Quasinormal modes on Kerr spacetimes

本文在次极值Kerr时空上建立严格框架，将准正规模式定义为时间平移生成元的孤立特征值，并给出Kerr–de Sitter的一致预解式估计、截断预解式亚纯延拓及准正规频率的稳定性与收敛性结果。

Mode stability and shallow quasinormal modes of Kerr-de Sitter black holes away from extremality

A Kerr-de Sitter black hole is a solution $(M,g_{Λ,\mathfrak{m},\mathfrak{a}})$ of the Einstein vacuum equations with cosmological constant $Λ>0$. It describes a black hole with mass $\mathfrak{m}>0$ and specific angular momentum $\mathfrak{a}\in\mathbb{R}$. We show that for any $ε>0$ there exists $δ>0$ so that mode stability holds for the linear scalar wave equation $\Box_{g_{Λ,\mathfrak{m},\mathfrak{a}}}ϕ=0$ when $|\mathfrak{a}/\mathfrak{m}|\in[0,1-ε]$ and $Λ\mathfrak{m}^2<δ$. In fact, we show that all quasinormal modes $σ$ in any fixed half space $\Imσ>-C\sqrtΛ$ are equal to $0$ or $-i\sqrt…

Kerr-de Sitter 时空中的波动方程：完整次极值范围

Wave equations in the Kerr-de Sitter spacetime: the full subextremal range

本文在完整次极值 Kerr-de Sitter 时空中证明了线性波动方程解的拟正规模态渐近展开，通过新的 Fredholm 框架和类光测地线 trapping 分析，将衰减问题归结为模态稳定性问题。