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arXiv 2501.02522gr-qc
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自旋s=0情形下克尔黑洞的伪谱

The pseudospectrum for the Kerr black hole with spin $s=0$ case

Rong-Gen Cai, Li-Ming Cao, Jia-Ning Chen, Zong-Kuan Guo, Liang-Bi Wu, Yu-Sen Zhou

AI总结:

本文利用超boloidal框架和二维切比雪夫配点法研究自旋s=0克尔黑洞的伪谱,揭示QNM频谱不稳定性,并分析不同导数阶范数下伪谱的收敛性及复频率虚部的影响。

摘要:

我们研究了克尔黑洞的伪谱,该伪谱揭示了克尔黑洞准正则模(QNMs)频谱的不稳定性。在方法上,我们采用超boloidal框架将QNM问题转化为与非自伴算子相关的二维特征值问题,然后通过施加二维切比雪夫配点法求解频谱和伪谱。对于自旋s=0情形,利用守恒流方法构造(能量)范数。对于算子的有限秩近似,我们讨论了使用不同范数(各自涉及不同阶导数)时伪谱的收敛性。随着导数阶数的增加,伪谱的收敛性得到改善。我们发现,在相同范数条件下,复频率虚部的增大会使伪谱的收敛性变差。

英文摘要:

We investigate the pseudospectrum of the Kerr black hole, which indicates the instability of the spectrum of quasinormal modes (QNMs) of the Kerr black hole. Methodologically, we use the hyperboloidal framework to cast the QNM problem into a two-dimensional eigenvalue problem associated with a non-self-adjoint operator, and then the spectrum and pseudospectrum are solved by imposing the two-dimensional Chebyshev collocation method. The (energy) norm is constructed by using the conserved current method for the spin $s=0$ case. For the finite rank approximation of the operator, we discuss the convergence of pseudospectra using various norms, each involving different orders of derivatives. The convergence of the pseudospectrum improves as the order of the derivatives increases. We find that an increase in the imaginary part of complex frequency can deteriorate the convergence of the pseudospectrum under the condition of the same norms.

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