AI 中文总结
该研究通过纽曼 - 贾尼斯算法得到新型克尔 - 赫恩quist黑洞解，利用解析渐近匹配方法研究其标量场动力学，推导准束缚态谱等，揭示了暗物质晕对黑洞谱和稳定性的影响，为相关研究提供统一框架。
AI 中文摘要
我们提出了一种由赫恩quist暗物质晕包围的新型旋转黑洞解，通过将纽曼 - 贾尼斯算法应用于精确的史瓦西 - 赫恩quist时空得到。所得的克尔 - 赫恩quist几何为研究现实暗物质环境中的标量场动力学提供了轴对称背景。利用解析渐近匹配方法，我们推导了准束缚态谱，确定了标量云形成和黑洞炸弹不稳定性的条件，并得到了超辐射散射放大因子的解析表达式。我们表明，暗物质晕保留了准束缚态谱的类氢结构，同时引入了由组合\(\rho_0 r_0^3\)控制的修正。增加暗物质晕密度和尺度半径会增强标量场结合能，降低标量云形成的临界场质量，抑制共旋转模式（\(m_\ell>0\)）的超辐射不稳定性增长率，并加速反向旋转模式（\(m_\ell<0\)）的衰减。此外，暗物质晕降低了超辐射放大的幅度和频率范围，从而削弱了从黑洞提取的能量。这些结果表明，克尔 - 赫恩quist几何为研究准束缚态、标量云、黑洞炸弹和超辐射散射提供了一个统一框架，同时揭示了赫恩quist暗物质晕如何在旋转黑洞的谱和稳定性上留下可观测的印记。
英文摘要
We present a novel rotating black hole solution surrounded by a Hernquist dark matter halo, obtained by applying the Newman--Janis algorithm to the exact Schwarzschild--Hernquist spacetime. The resulting Kerr--Hernquist geometry provides an axisymmetric background for investigating scalar-field dynamics in realistic dark matter environments. Using the analytical asymptotic matching method, we derive the quasibound-state spectrum, identify the conditions for scalar cloud formation and the black hole bomb instability, and obtain an analytic expression for the superradiant scattering amplification factor. We show that the halo preserves the hydrogen-like structure of the quasibound-state spectrum while introducing corrections governed by the combination $ρ_0 r_0^3$. Increasing the halo density and scale radius enhances the scalar-field binding energy, lowers the critical field mass for scalar cloud formation, suppresses the growth rate of the superradiant instability for co-rotating modes ($m_\ell>0$), and accelerates the decay of counter-rotating modes ($m_\ell<0$). Furthermore, the dark matter halo reduces both the magnitude and frequency range of superradiant amplification, thereby weakening energy extraction from the black hole. These results demonstrate that the Kerr--Hernquist geometry provides a unified framework for studying quasibound states, scalar clouds, black hole bombs, and superradiant scattering, while revealing how a Hernquist dark matter halo leaves observable imprints on the spectrum and stability of rotating black holes.
CommentsThe authors are withdrawing this manuscript to allow for further analysis and validation of the results. Additional investigation is required to ensure the robustness of the conclusions before resubmission
