发表机构
University of Jinan; Institute of Theoretical Physics, Chinese Academy of Sciences; Ningbo University（济南大学; 中国科学院理论物理研究所; 宁波大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Kerr黑洞引力扰动（自旋权重s=2）的伪谱，利用Teukolsky-Starobinsky恒等式构造H^2能量范数，发现伪谱在L^2→H^1→H^2逐级收紧但仍大，且s=+2与s=-2不等伪谱，引力扰动谱不稳定性强于标量情形。
AI 中文摘要
我们研究了Kerr黑洞在自旋权重$s=2$的引力扰动下的伪谱，这是引力波天文学中最受关注的情形。在双曲框架下采用二维切比雪夫配点法，我们将准正则模问题表述为非自伴特征值问题。对于$s\neq0$，场$\Psi^{(s)}$和$\Psi^{(-s)}$是独立的，因此守恒流方法无法给出单场能量范数。我们通过Teukolsky--Starobinsky恒等式克服了这一困难，该恒等式将$\Psi^{(-2)}$与$\Psi^{(2)}$上的四阶算子联系起来，并在对称化后得到$H^2$能量范数。已知$s=0$时的$H^1$范数，这暗示了$H^{|s|}$的模式，并已在$s=0$和$s=2$情形下得到验证。所有结果均使用与$\omega$无关的两场层级。我们发现，在$L^2\to H^1\to H^2$的每一步中，伪谱收紧1.1到3.5个数量级，但在每种范数下仍然较大。$s=+2$和$s=-2$算子等谱但不等伪谱：在十四个探测点中的十二个点上，$\psi_0$预解式在$H^2$范数下比$\psi_4$预解式大0.19到0.82个数量级，而在沿QNM线最远的两个探测点上，顺序反转，相差0.18到0.19个数量级。引力伪谱在窗口最小值处比标量伪谱大0.5到5.2个数量级，在$\omega M=0.47-0.17\\,i$处的$L^2$范数下大5.9个数量级，而沿阻尼方向，$s=2$预解式非单调，$s=0$预解式平滑。因此，QNM谱不稳定性是Kerr黑洞的普遍特征，且对引力扰动更强。
英文摘要
We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight $s=2$, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For $s\neq0$ the fields $Ψ^{(s)}$ and $Ψ^{(-s)}$ are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky--Starobinsky identities, which relate $Ψ^{(-2)}$ to a fourth-order operator on $Ψ^{(2)}$ and yield an $H^2$ energy norm after symmetrization. With the $H^1$ norm known for $s=0$, this suggests the pattern $H^{|s|}$, verified for $s=0$ and $s=2$. All results use an $ω$-independent two-field hierarchy. We find that the pseudospectrum tightens by $1.1$ to $3.5$ decades at each step of $L^2\to H^1\to H^2$, yet stays large in every norm. The $s=+2$ and $s=-2$ operators are isospectral but not isopseudospectral: at twelve of fourteen probes the $ψ_0$ resolvent exceeds the $ψ_4$ one by $0.19$ to $0.82$ decades in the $H^2$ norm, while at the two probes furthest along the QNM line the ordering reverses by $0.18$ to $0.19$ decades. The gravitational pseudospectrum exceeds the scalar one by $0.5$ to $5.2$ decades in the window minimum and by $5.9$ decades in $L^2$ at $ωM=0.47-0.17\,i$, while along the damping direction the $s=2$ resolvent is non-monotonic and the $s=0$ resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.
Comments67 pages, 8 figures
