AI 中文总结
研究大黄蜂引力中四维渐近反德西特黑洞的洛伦兹对称性破缺，通过分析标量波传播等构建有效折射率，结合热力学分析，将黑洞建模为热机，构建显式循环，揭示其与洛伦兹违反等多方面的联系及效率变化。
AI 中文摘要
我们研究了自发洛伦兹对称性破缺对四维渐近反德西特黑洞在大黄蜂引力中标量波传播、零测地线和热力学行为的影响。静态球对称解由一个无量纲参数$\ell > -1$表征，它源于大黄蜂矢量场的真空期望值，全局重新缩放径向几何。通过将径向克莱因 - 戈登方程转化为广义亥姆霍兹形式分析无质量标量场，得到有效频率依赖折射率，确定振荡和消逝区域、经典转折点以及由曲率和洛伦兹违反引起的限制。在高频极限下，波传播与零测地线一致，$\ell$控制径向缩放并支配几何光学极限。反德西特边界反射波，视界充当单向吸收器。非扩展和扩展相空间的热力学分析证实了第一定律和斯马尔关系，$\ell$影响热容量、自由能和稳定性。将这些黑洞建模为热机，我们构建了显式循环并表明效率随$\ell$增加，导致$\eta \leq 1$的上限。我们的结果提供了一个框架，将大黄蜂引力中的洛伦兹违反、波传播、几何光学和反德西特黑洞热力学联系起来。
英文摘要
We investigate the impact of spontaneous Lorentz symmetry breaking on scalar wave propagation, null geodesics, and thermodynamic behavior of four-dimensional asymptotically AdS black holes in bumblebee gravity. The static, spherically symmetric solutions are characterized by a dimensionless parameter $\ell > -1$ arising from the vacuum expectation value of the bumblebee vector field, which globally rescales the radial geometry. Massless scalar fields are analyzed via the radial Klein--Gordon equation cast into a generalized Helmholtz form, yielding an effective frequency-dependent refractive index that identifies oscillatory and evanescent regions, classical turning points, and confinement induced by curvature and Lorentz violation. In the high-frequency limit, wave propagation coincides with null geodesics, with $\ell$ controlling radial scaling and governing the geometric-optics limit. The AdS boundary reflects waves, while the horizon acts as a one-way absorber. Thermodynamic analysis in non-extended and extended phase spaces confirms the first law and Smarr relation, with $\ell$ influencing heat capacity, free energy, and stability. \textcolor{black}{Modeling these black holes as heat engines, we construct explicit cycles and show that efficiency increases with $\ell$, leading to an upper bound imposed by $η\leq 1$. Our results provide a framework connecting Lorentz violation, wave propagation, geometric optics, and AdS black hole thermodynamics in bumblebee gravity.
Journal refChin. J. Phys. 103, 1698-1713, (2026)
DOI：10.1016/j.cjph.2026.07.024
