具有非最小对数耦合的黑洞的量子修正热力学、狄拉克微扰、测地线结构和拓扑相
Quantum-Corrected Thermodynamics, Dirac Perturbations, Geodesic Structure, and Topological Phases of Black Holes with Non-Minimal Logarithmic Coupling
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中文总结 AI 辅助
研究非最小对数耦合修正的爱因斯坦 - 麦克斯韦理论中黑洞性质，用费米子隧穿等方法获霍金温度等，构建量子几何修正相空间并表征拓扑相结构，发现有效压力在拓扑缺陷线消失，关联压力与局部稳定性。
中文摘要 AI 辅助
我们研究了由非最小$\ln(R)F^{2}$耦合修正的爱因斯坦 - 麦克斯韦理论中静态、球对称黑洞的热力学和动力学性质。通过费米子隧穿方法的哈密顿 - 雅可比形式得到霍金温度，其带有与尺度相关的对数修正。分析了无质量狄拉克场的传播，用三阶WKB近似计算准正则模（QNM）谱并得出品质因子。研究了费米子场的透射及其霍金辐射，求解了零测地线和类时测地线问题以得到光子球、阴影半径等。通过巴罗熵构建了具有量子几何修正的相空间，用拓扑方法表征全局相结构。发现有效压力恰好在拓扑缺陷线上消失，该线将压力符号与各分支的局部稳定性联系起来。
英文摘要
We study the thermodynamic and dynamical properties of static, spherically symmetric BHs in Einstein-Maxwell theory modified by a non-minimal $\ln(R)F^{2}$ coupling. The Hawking temperature follows from the Hamilton-Jacobi form of the fermionic tunnelling method for spin-$\tfrac12$ particles, and it carries scale-dependent logarithmic corrections. We then analyze the propagation of massless Dirac fields, compute the quasinormal-mode (QNM) spectrum with the third-order WKB approximation, and read off a quality factor whose balance between oscillation and damping depends on the logarithmic coupling in a mode-dependent way. Moving outward from the horizon, we work out the transmission of the fermionic field and its Hawking emission, and we solve the null and timelike geodesic problems to obtain the photon sphere, the shadow radius, the innermost stable circular orbit (ISCO), the associated zoom-whirl bound orbits, and the orbital and epicyclic frequencies that set the twin-peak quasiperiodic-oscillation (QPO) ratio. A photon-sphere reading of the eikonal QNM frequencies ties the geodesic sector back to the field perturbations. On the thermodynamic side, we build the phase space with quantum-geometric corrections through the Barrow entropy, and we characterize the global phase structure with the topological method, where the winding numbers of the off-shell free energy are governed by the interplay of the fractal Barrow deformation, the electric charge, and the logarithmic coupling. We find that the effective pressure vanishes exactly on the topological defect line, which links the pressure sign to the local stability of each branch.
