热力学、热力学几何及Kiselev流体包围的Bardeen黑洞的阴影：正则性、渐近性与观测自洽性的作用
Thermodynamics, thermodynamic geometry, and the shadow of a Bardeen black hole surrounded by a Kiselev fluid: the role of regularity, asymptotics, and observational self-consistency
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中文总结 AI 辅助
本研究重新分析Kiselev流体包围的Bardeen黑洞，发现其正则性与渐近性依赖参数c，推导修正熵并验证热力学定律，识别热力学几何中的伪影，并指出EHT对c的约束仅限视界附近而非宇宙学尺度。
中文摘要 AI 辅助
我们重新考虑了由Kiselev流体包围的Bardeen黑洞，该解是通过在Ayon-Beato-Garcia-Bardeen度规中加入Kiselev项而得到的。与文献中的说法相反，该解仅在$c=0$时在原点处正则：对于$c\neq0$，曲率不变量在$r\to0$时发散，且时空渐近为类de Sitter而非平坦，对于$0<c<c_N(q)$存在宇宙视界$r_c$。我们以闭合形式描绘了完整的$(q,c)$视界结构域，定位了极端边界和Nariai型边界及其尖点。利用Ma-Zhao关于质量相关非线性电动力学源的方案，我们推导了修正的熵，并通过计算机代数微分而非熵自身的定义，验证了扩展第一定律和Smarr关系到机器精度。热容显示出单个Davies型发散，以闭合形式四次方程定位并在$c$中解析展开。在热力学几何中，Quevedo度规曲率具有由熵的积分常数及其共形因子的非唯一性产生的虚假第二奇点；我们隔离了这一伪影，并表明只有Davies点发散是物理的。Ruppeiner曲率对于纯Bardeen恒为零，一旦$c\neq0$则变为非零。对于阴影，我们计算了临界冲击参数$b_c(q,c,w)$，并表明来自人马座A*的EHT图像的标称界限$c\backsimeq10^{-2}/M$并非自洽：相同的$c$使宇宙视界比地球到Sgr A*的距离近九个数量级，且该界限比真正的宇宙暗能量尺度$H_0/c$大十四个数量级。我们将EHT约束重新解释为仅限制视界附近的$c$，而非对quintessence参数的天体物理或宇宙学界限。
英文摘要
We reconsider the Bardeen black hole surrounded by a Kiselev fluid, obtained by adding a Kiselev term to the Ayon-Beato-Garcia-Bardeen metric. Contrary to claims in the literature, the solution is regular at the origin only for $c=0$: for $c\neq0$ curvature invariants diverge as $r\to0$, and the spacetime is asymptotically de Sitter-like rather than flat, with a cosmological horizon $r_c$ for $0<c<c_N(q)$. We map the full $(q,c)$ domain of horizon structures in closed form, locating the extremal and Nariai-type boundaries and their cusp. Using the Ma-Zhao prescription for the mass-dependent nonlinear-electrodynamics source, we derive the corrected entropy and verify the extended first law and Smarr relation to machine precision by computer-algebra differentiation, not through the entropy's own definition. The heat capacity shows a single Davies-type divergence, located as a closed-form quartic and expanded analytically in $c$. In thermodynamic geometry, the Quevedo-metric curvature has a spurious second singularity generated by the entropy's integration constant and the non-uniqueness of its conformal factor; we isolate this artefact and show only the Davies-point divergence is physical. The Ruppeiner curvature, identically zero for pure Bardeen, becomes non-zero once $c\neq0$. For the shadow, we compute the critical impact parameter $b_c(q,c,w)$ and show the nominal bound $c\lesssim10^{-2}/M$ from the EHT image of Sagittarius A* is not self-consistent: the same $c$ places the cosmological horizon nine orders of magnitude closer than Earth's distance to Sgr A*, and the bound is fourteen orders of magnitude larger than $H_0/c$, the true cosmological dark-energy scale. We reinterpret the EHT constraint as bounding $c$ only near the horizon, not as an astrophysical or cosmological bound on the quintessence parameter.
发表机构
- Hanoi Pedagogical University 2（河内师范大学二校）
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