Kalb-Ramond-ModMax黑洞的分支结构与非广延热力学：观测特征
Branch structure and nonextensive thermodynamics of Kalb-Ramond-ModMax black holes: observational signatures
AI总结：
研究Kalb-Ramond-ModMax黑洞的分支结构及非广延热力学，探讨其观测特征，通过EHT数据约束框架。
摘要：
受异质弦理论低能有效动作启发，其中Kalb-Ramond二形式和非线性规范修正同时出现，我们研究了爱因斯坦引力与Kalb-Ramond场及ModMax非线性电磁动力学耦合的静态球对称黑洞解。该解除质量与电荷外，还依赖于洛伦兹对称破缺参数ℓ、ModMax变形参数γ及离散分支选择器ζ=±1。我们证明普通分支允许极值和非极值配置，而虚幻分支通常支持单一视界几何。黑洞热力学在Tsallis非广延框架下分析，揭示分支依赖的稳定性及焦耳-汤姆逊行为。通过Ono-Ishihara-Asada扩展的Gauss-Bonnet定理计算弱引力透镜效应，得出负拓扑修正，使光弯曲程度低于Schwarzschild基线，符号与Barriola-Vilenkin单极背景相反。研究等离子体环境中的光球性质及潮汐力通过测地偏离，揭示普通分支中普遍的潮汐平衡比R_rad/R_ang=3/2。这些多通道特征为通过事件视界望远镜(EHT)数据及下一代干涉仪阵列约束KR-ModMax框架提供具体观测依据。
英文摘要：
Motivated by the low-energy effective action of heterotic string theory, where the Kalb-Ramond (KR) two-form and nonlinear gauge corrections arise simultaneously, we investigate a static, spherically symmetric black hole (BH) in Einstein gravity coupled to a KR field and ModMax nonlinear electrodynamics (NED). The solution depends, beyond mass and charge, on the Lorentz-symmetry-breaking (LSB) parameter $\ell$, the ModMax deformation parameter $γ$, and a discrete branch selector $ζ=\pm1$. We show that the ordinary branch admits extremal and non-extremal configurations, while the phantom branch generically supports a single-horizon geometry. BH thermodynamics is analyzed within the Tsallis non-extensive framework, revealing branch-dependent stability and Joule-Thomson (JT) behavior. Weak gravitational lensing is computed via the Ono-Ishihara-Asada (OIA) extension of the Gauss-Bonnet (GB) theorem, yielding a negative topological correction that reduces light bending relative to the Schwarzschild baseline, opposite in sign to Barriola-Vilenkin (BV) monopole backgrounds. Photon sphere (PS) properties in plasma environments and tidal forces through geodesic deviation are also studied, revealing a universal tidal balance ratio $R_{\rm rad}/R_{\rm ang}=3/2$ in the ordinary branch. These multi-channel signatures provide concrete observational handles for constraining the KR-ModMax framework through Event Horizon Telescope (EHT) data and next-generation interferometric arrays.
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