AI 中文总结
该研究结合经典几何与量子场论约束，基于量子聚焦猜想，推导出广义膨胀的微分不等式，揭示膨胀与剪切在控制熵流中的作用，明确量子极值面相关性质，推导类光生成元分离界，为半经典引力熵界提供局部几何细化。
AI 中文摘要
我们开发了一个局部协变框架来约束沿类光视界的广义熵演化，将经典几何方法与量子场论的约束相结合。基于限制沿类光方向熵演化的量子聚焦猜想（QFC），我们推导出一个关于广义膨胀的瑞查德利型微分不等式，明确了其对膨胀和剪切的局部依赖性。所得关系$\frac{d\Theta}{d\lambda} \le -\theta \Theta + \tfrac{1}{2}\theta^2 - \sigma^2$揭示了膨胀和剪切在控制熵流中的直接相互作用。我们进一步表明量子极值面对应于$\Theta = 0$的构型，其局部稳定性由相同几何数据决定。此外，我们推导了附近类光生成元指数分离的界。我们的结果为半经典引力中的熵界提供了局部几何细化，并建立了类光几何、量子能量条件和熵流之间的直接联系。
英文摘要
We develop a local and covariant framework for constraining the evolution of generalized entropy along null horizons, combining classical geometric methods with constraints from quantum field theory. Building on the quantum focusing conjecture (QFC), which restricts entropy evolution along null directions, we derive a Raychaudhuri-type differential inequality for the generalized expansion that makes its local dependence on expansion and shear explicit. The resulting relation, $\frac{dΘ}{dλ} \le -θΘ+ \tfrac{1}{2}θ^2 - σ^2$, reveals a direct interplay between expansion and shear in controlling entropy flow: shear contributes negatively and yields a monotonic suppression of the generalized expansion in shear-dominated regimes, while expansion provides a competing geometric source term. This structure provides a local geometric formulation consistent with the QFC and clarifies its interpretation as a constraint on entropy evolution. We further show that quantum extremal surfaces correspond to configurations characterized by $Θ=0$, whose local stability properties are governed by the same geometric data. In addition, we derive a bound on the exponential separation of nearby null generators, indicating that the same combination of expansion and shear also controls geometric instability. Our results provide a local geometric refinement of entropy bounds in semiclassical gravity and establish a direct connection between null geometry, quantum energy conditions, and entropy flow, offering a local geometric perspective on horizon thermodynamics beyond global formulations.
Comments17 pages, published in Physical Review D
Journal refPhys. Rev. D 114, 023524 (2026)
