AI 中文总结
本研究构建含修正恰普林气体包层的三区旋转致密天体时空模型，发现嵌于致密MCG结构的黑洞可提升辐射效率，为量化黑洞自旋估计的环境系统不确定性提供了新框架。
AI 中文摘要
视界尺度观测的理论解释常依赖孤立真空克尔几何的理想化假设，但天体物理黑洞预计嵌于致密暗物质分布中，可修改局域时空几何。本研究提出一个理论框架，用以建模被受修正恰普林气体（Modified Chaplygin Gas, MCG）状态方程支配的有界暗物质包层环绕的旋转致密天体。为严格满足爱因斯坦场方程，我们采用完全耦合的托尔曼-奥本海默-沃尔科夫（Tolman-Oppenheimer-Volkoff, TOV）积分构造分段式三区时空，使流体压强自然衰减至零并动态定义外边界；通过压强修正的克尔形式假设引入旋转，其中时间分量直接由积分的流体静力学势得到。利用该几何严格的构型（其明确计算精确四维赤道度规行列式，而非依赖真空近似），我们求解赤道圆轨道并确定最内稳定圆轨道（innermost stable circular orbit, ISCO）。通过诺维科夫-索恩（Novikov-Thorne）形式主义评估薄吸积盘热力学，发现MCG包层的深引力势阱是黏性耗散的强驱动因素，系统性地将热通量峰值、有效温度及多色黑体光谱光度移至更高能带。此外，我们识别出明确的结构简并：嵌于致密MCG结构中的静态或缓慢旋转黑洞可将辐射效率提升至η≈6.5%。该框架作为结构化提议，用于量化标准黑洞自旋估计技术中的环境系统不确定性。
英文摘要
Theoretical interpretations of horizon-scale observations often rely on the idealized assumption of an isolated vacuum Kerr geometry. However, astrophysical black holes are expected to be embedded within dense dark matter distributions that can modify the local spacetime geometry. In this work, we propose a theoretical framework to model a rotating compact object surrounded by a bounded dark matter envelope governed by a Modified Chaplygin Gas (MCG) equation of state. To ensure strict adherence to the Einstein Field Equations, we construct a piece-wise, three-region spacetime using a fully coupled Tolman-Oppenheimer-Volkoff (TOV) integration, allowing the fluid's pressure to taper naturally to zero and dynamically define the outer boundary. Rotation is introduced via a pressure-corrected Kerr-form ansatz where the temporal component is obtained directly from the integrated hydrostatic potential. Using this geometrically rigorous configuration, which explicitly evaluates the exact 4D equatorial metric determinant rather than relying on vacuum approximations, we solve the circular equatorial geodesics and determine the innermost stable circular orbit (ISCO). Evaluating the thin accretion disk thermodynamics via the Novikov-Thorne formalism reveals that the deep gravitational potential well of the MCG envelope acts as a strong driver for viscous dissipation, systematically shifting the peak thermal flux, effective temperature, and multi-colour blackbody spectral luminosity to higher energy bands. Furthermore, we identify a clear structural degeneracy: a static or slowly rotating black hole embedded in a dense MCG structure can elevate radiative efficiencies up to $η\approx 6.5\%$. This framework is presented as a structured proposal to quantify environmental systematic uncertainties in standard black hole spin-estimation techniques.
Comments15 pages, 10 figures
