AI 中文总结
研究克尔-贝托蒂-罗宾逊黑洞的光学和热力学性质，通过推导相关量、引入新解释、计算质量电荷及推导多种参数，得出该背景对黑洞多种性质有影响，如减小能层厚度和阴影面积等。
AI 中文摘要
我们研究克尔-贝托蒂-罗宾逊黑洞的热力学和光学性质，即处于外部贝托蒂-罗宾逊电磁背景中的旋转黑洞。在固定\(a\)系综中，我们推导了视界质量关系、霍金温度、熵、亥姆霍兹型自由能、热容量和极值残余构型。当\(B\to0\)时，这些量平滑地还原为克尔对应量。在弱场 regime，主要的热力学修正出现在\(B^2\)阶；极值半径在此阶移动，而残余质量仅在\(B^4\)阶接受其首次修正。我们还引入了对贝托蒂-罗宾逊尺度的形式上类似反德西特的热力学解释，将相关压力视为有效响应变量而非真正的宇宙学压力。由于时空不是渐近平坦的，我们进一步计算了与视界生成元相关的有限半径科马尔质量和科马尔电荷。使用哈密顿-雅可比形式，我们推导了分离的零测地线势、球形光子轨道的碰撞参数以及有限距离观察者的阴影边界的天球坐标。然后我们刻画了光子区域边界、能层厚度、光子-能层间隙、阴影面积和磁阴影敏感性。在考虑的微扰 regime 内，贝托蒂-罗宾逊背景减小了平均能层厚度和阴影面积，增加了光子-能层间隙，并产生了负阴影敏感性，其大小因旋转而增强。
英文摘要
We investigate the thermodynamic and optical properties of Kerr--Bertotti--Robinson black holes, namely rotating black holes immersed in an external Bertotti--Robinson electromagnetic background. In the fixed-$a$ ensemble, we derive the horizon mass relation, the Hawking temperature, the entropy, the Helmholtz-type free energy, the heat capacity, and the extremal remnant configuration. These quantities reduce smoothly to their Kerr counterparts as $B\to0$. In the weak-field regime, the leading thermodynamic corrections arise at order $B^2$; the extremal radius is shifted at this order, whereas the remnant mass receives its first correction only at order $B^4$. We also introduce a formal AdS-like thermodynamic interpretation of the Bertotti--Robinson scale, treating the associated pressure as an effective response variable rather than a genuine cosmological pressure. Because the spacetime is not asymptotically flat, we further compute the finite-radius Komar mass and the Komar charge associated with the horizon generator. Using the Hamilton--Jacobi formalism, we derive the separated null-geodesic potentials, the impact parameters of spherical photon orbits, and the celestial coordinates of the shadow boundary for a finite-distance observer. We then characterize the photon-region boundaries, ergosphere thickness, photon--ergosphere gap, shadow area, and magnetic shadow susceptibility. Within the perturbative regime considered, the Bertotti--Robinson background decreases the averaged ergosphere thickness and shadow area, increases the photon--ergosphere gap, and produces a negative shadow susceptibility whose magnitude is enhanced by rotation.
