AI 中文总结
该研究推导并测试了静态f(R,T)黑洞纯电分支中带电能量提取的运动学边界，对比了不同背景的能量提取特性，明确了视界电势与渐近结构对能量提取的影响。
AI 中文摘要
我们推导并测试了由欧拉-海森堡型非线性电磁扇区产生的静态f(R,T)黑洞家族纯电分支中带电能量提取的运动学上限边界。分析仅限于固定背景下外部、最小耦合的探针粒子。在该电解中，场保持库仑形式直至附加规范常数；因此非线性电磁和物质耦合系数通过度规、事件视界位置及全局因果结构间接影响能量提取。我们获得了保留负能量碎片非零角动量和径向速度的一般局域边界，并将常用的零角动量转向点选择确定为上包络而非一般衰变构型。共动拆分提供了局域四动量守恒基准。我们用重根条件F=F'=0对视界进行分类，区分渐近平直、德西特和反德西特分支，并施加相应的全局向外可达性判据。在德西特静态 patch 中，静电能以宇宙学视界为参考，因此相关尺度为Q(1/r₊ - 1/r_c)而非Q/r₊。可复现扫描对比了雷斯纳-诺德斯特龙、爱因斯坦-欧拉-海森堡型、f(R,T)-麦克斯韦及全f(R,T)-欧拉-海森堡型背景。结果表明，分支参考的视界电势控制局域上包络，而渐近结构决定向外轨迹能否到达无穷远、宇宙学视界或仅有限外转向点。
英文摘要
We derive and test kinematic upper bounds on charged energy extraction in the purely electric branch of a static $f(R,T)$ black hole family sourced by an Euler--Heisenberg type nonlinear electromagnetic sector. The analysis is restricted to external, minimally coupled probe particles on the fixed background. In this electric solution the field remains Coulombic up to an additive gauge constant; the nonlinear electromagnetic and matter-coupling coefficients therefore affect extraction indirectly through the metric, the event-horizon position, and the global causal structure. We obtain a general local bound retaining nonzero angular momentum and radial velocity of the negative energy fragment, and identify the commonly used zero angular momentum turning-point choice as an upper envelope rather than a generic decay configuration. A co-moving split supplies a locally four momentum-conserving benchmark. We classify horizons with the double root conditions $\mathcal F=\mathcal F'=0$, distinguish asymptotically flat, de Sitter, and anti-de Sitter branches, and impose the corresponding global outward-accessibility criterion. In the de Sitter static patch the electrostatic energy is referenced to the cosmological horizon, so the relevant scale is $Q(1/r_+-1/r_c)$ rather than $Q/r_+$. Reproducible scans compare Reissner--Nordström, Einstein--Euler--Heisenberg type, $f(R,T)$--Maxwell, and full $f(R,T)$--Euler--Heisenberg type backgrounds. The results show that the branch-referenced horizon potential controls the local upper envelope, whereas the asymptotic structure determines whether an outward trajectory can reach infinity, a cosmological horizon, or only a finite outer turning point.
