A model problem for quasinormal ringdown of asymptotically flat or extremal black holes
A model problem for quasinormal ringdown of asymptotically flat or extremal black holes
复制标题
渐近平坦黑洞或极值黑洞的拟正态衰减模型问题
DOI：
10.1063/5.0024699
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发表时间：
2019
影响因子：
1.3
通讯作者：
C. Warnick
中科院分区：
文献类型：
--
作者：
D. Gajic;C. Warnick
我们考虑一个在半直线上有位势的波动方程，作为波在黑洞时空的极值视界或渐近平坦末端附近传播的模型问题。给出了作用于适当的(基于Gevrey的)Hilbert空间上的零叶变换的时间平移生成元的本征值的准正规频率的定义。我们证明了这个QNF谱在{C}$的子集上是离散的，它包括任意$b>；0$的区域$$Re$(S)>；-b$，$|$Im$(S)|>；K$和一些$K=K(B)\gg1$。作为推论，我们建立了扇形{|$Arg$(S)|\FRAC{2\pi}{3}$中散射预解器的亚纯性，并证明了极点只出现在我们定义的准正规频率上。这一结果适用于复数标度法不能直接应用的情况，因为我们的势不必是解析的。最后，我们证明了根据我们的新定义，用Leaver的连分式方法计算的QF必然是QF。本文是对[D.Gajic和C.Warnick，Quasinormal Modes in Extremal Reissner-Nordstrom Spacetime，Preprint(2019)]的补充，后者研究了极值Reissner-Nordstrom黑洞波动方程的准正则模。
We consider a wave equation with a potential on the half-line as a model problem for wave propagation close to an extremal horizon, or the asymptotically flat end of a black hole spacetime. We propose a definition of quasinormal frequencies (QNFs) as eigenvalues of the generator of time translations for a null foliation, acting on an appropriate (Gevrey based) Hilbert space. We show that this QNF spectrum is discrete in a subset of $\mathbb{C}$ which includes the region $\{$Re$(s) >-b$, $|$Im $(s)|> K\}$ for any $b>0$ and some $K=K(b) \gg 1$. As a corollary we establish the meromorphicity of the scattering resolvent in a sector $|$arg$(s)| \frac{2\pi}{3}$, and show that the poles occur only at quasinormal frequencies according to our definition. This result applies in situations where the method of complex scaling cannot be directly applied, as our potentials need not be analytic. Finally, we show that QNFs computed by the continued fraction method of Leaver are necessarily QNFs according to our new definition. This paper is a companion to [D. Gajic and C. Warnick, Quasinormal modes in extremal Reissner-Nordstrom spacetimes, preprint (2019)], which deals with the QNFs of the wave equation on the extremal Reissner-Nordstrom black hole.
通过 Gevrey-2 Properties 输出解决方案
影响因子：
2.8
作者：
Galkowski, Jeffrey;Zworski, Maciej
通讯作者：
Zworski, Maciej