一般双幂律暗物质环境下的新型类克尔黑洞：几何、光谱学与能量提取
A Novel Kerr-like Black Hole in a General Double Power Law Dark Matter Environment: Geometry, Spectroscopy, and Energy Extraction
中文总结 AI 辅助
该研究构建了一般双幂律暗物质环境下的新型类克尔黑洞解，分析其几何、光谱特征及能量提取效率，揭示暗物质对黑洞性质的影响。
中文摘要 AI 辅助
我们通过将Newman–Janis算法应用于类史瓦西种子几何，构建了嵌入一般双幂律暗物质环境的新型类克尔黑洞解。该框架为任意双幂律密度分布提供了统一的旋转时空，并揭示了暗物质如何修改旋转黑洞的视界结构、极端自旋和曲率性质。值得注意的是，我们发现，对于γ≤2的Dehnen型分布，旋转与暗物质晕的相互作用可消除基本曲率奇点，尽管对应静态配置具有奇异性。随后，我们通过Dehnen(1,4,γ)晕中的大质量标量扰动，研究暗物质环境的光谱特征。采用解析低频匹配方法，我们推导了准束缚态谱、标量云形成的起始条件以及超辐射放大因子，表明晕参数ρ₀r₀³和γ在标量谱上留下了特征印记。增加晕密度或尖度会增强准束缚态的束缚性并加快其衰减，改变标量云阈值，且通过缩小允许的频率窗口并降低放大因子峰值，抑制超辐射放大的有效性。最后，我们分析了从热标量场提取旋转能量的过程，证明效率由热谱与超辐射不稳定性的相互作用控制，较低温度和较不尖的密度分布会产生更高效的能量提取。
英文摘要
We construct a novel Kerr-like black hole solution embedded in a general double power law dark matter environment by applying the Newman--Janis algorithm to a Schwarzschild-like seed geometry. This framework provides a unified rotating spacetime for arbitrary double power law density profiles and reveals how dark matter modifies the horizon structure, extremal spin, and curvature properties of rotating black holes. Remarkably, we find that the rotation--halo interplay can eliminate essential curvature singularities for Dehnen-type profiles with $γ\leq2$, despite the singular nature of the corresponding static configurations. We then investigate the spectroscopic signatures of the dark matter environment through massive scalar perturbations in the Dehnen $(1,4,γ)$ halo. Using an analytical low-frequency matching method, we derive the quasibound state spectrum, the onset condition for scalar cloud formation, and superradiant amplification factor, showing that the halo parameters $ρ_0 r_0^3$ and $γ$ leave characteristic imprints on the scalar spectrum. Increasing the halo density or the cusp strengthens the binding of quasibound states and enhances their decay, shifts the scalar cloud threshold, and suppresses superradiant amplification effectivity by narrowing the allowed frequency window and lowering the amplification factor peak. Finally, we analyze rotational energy extraction from thermal scalar fields and demonstrate that the efficiency is controlled by the interplay between the thermal spectrum and the superradiant instability, with lower temperatures and less cuspy density profiles yielding more efficient energy extraction.
