AI 中文总结
本文研究Bumblebee引力中带整体单极的类Schwarzschild-de Sitter黑洞的测地线、QNMs与热力学，揭示洛伦兹破缺与拓扑缺陷对其的影响，验证程函QNMs与零测地线的对应关系，评估其作为全息热机的特性并得出相关约束。
AI 中文摘要
我们研究了Bumblebee引力中与整体单极耦合的类Schwarzschild-de Sitter黑洞的测地线动力学、程函类准正规模（QNMs）及扩展相空间热力学。分析表明，自发洛伦兹对称性破缺与拓扑缺陷会修改有效径向动力学，导致有效势垒降低、有效力的幅值减小。对于零测地线，更高的单极参数会扩展光子球与临界碰撞参数，意味着黑洞阴影增大，同时缓解动力学不稳定性；对于大质量粒子，随着最外层稳定圆轨道（OSCO）收缩，稳定圆轨道窗口显著变窄，近日点进动明显增强。此外，我们考察了程函类QNMs与零测地线性质的对应关系，程函近似与WKB方法对标量和电磁扰动的良好一致性，支持所研究时空的该对应关系成立。在扩展热力学相空间中，我们将黑洞作为全息热机进行评估，结果表明经典效率对洛伦兹破缺具有数学上的不可感知性；但引入量子修正的修正熵后，宏观功输出与对称性破缺框架紧密耦合。最终，遵守卡诺界的必要性对洛伦兹破缺参数施加了严格的宏观约束，保障了热力学第二定律。
英文摘要
We investigate the geodesic dynamics, eikonal quasinormal modes (QNMs), and extended phase space thermodynamics of a Schwarzschild-de Sitter-like black hole coupled with a global monopole in Bumblebee gravity. Our analysis reveals that spontaneous Lorentz symmetry breaking and topological defects modify the effective radial dynamics, leading to lower effective potential barriers and a reduced magnitude of the effective force. For null geodesics, higher monopole parameters expand the photon sphere and critical impact parameter, implying an enlarged black hole shadow, while mitigating dynamical instability. For massive particles, the stable circular orbit window narrows significantly as the Outermost Stable Circular Orbit (OSCO) shrinks, alongside a marked enhancement in perihelion precession. In addition, we examine the correspondence between the eikonal QNMs and the properties of null geodesics. The excellent agreement between the eikonal approximation and the WKB method for scalar and electromagnetic perturbations supports the validity of the correspondence for the spacetime under consideration. In the extended thermodynamic phase space, we evaluate the black hole as a holographic heat engine. We demonstrate that classical efficiency is mathematically blind to Lorentz violation; however, introducing a quantum-corrected modified entropy tightly couples the macroscopic work output to the symmetry-breaking framework. Ultimately, the necessity to respect the Carnot bound imposes a strict macroscopic constraint on the Lorentz-violating parameter, safeguarding the Second Law of Thermodynamics.
