AI 中文总结
该研究绕过时空微分同胚，将引力熵定义为局域横向洛伦兹变换相关的可积面电荷，类比牛顿力学，证明引力热力学第二定律由满足特定条件的自由下落观测者表述，并给出局域第二定律的证明。
AI 中文摘要
我们将引力熵定义为与局域横向洛伦兹变换相关的显式可积面电荷，完全绕过了对时空微分同胚的传统依赖。任何熵的概念都必须满足第二定律。为回答标题提出的问题，类比牛顿经典力学颇具启发：牛顿运动第二定律由惯性观测者表述，而惯性观测者由力学第一定律定义。我们证明，引力热力学第二定律由自由下落观测者表述，这类观测者的路径参数化中，测地线的非仿射性等于其速度矢量场的膨胀量。随后，我们通过研究这类协变定义的因果自由下落观测者视角下的熵变，给出局域第二定律的证明。我们表明，只要物质 sector 沿观测者路径满足积分强能量条件，熵变就严格非递减。
英文摘要
We define gravitational entropy as the manifestly integrable surface charge associated with local transverse Lorentz boosts, entirely bypassing the conventional reliance on spacetime diffeomorphisms. Any notion of entropy must satisfy the second law. To answer the question posed in the title, an analogy with Newtonian classical mechanics is instructive: Newton's second law of motion is written by inertial observers who are defined by the first law of mechanics. We show that the second law of gravitational thermodynamics is written by free-fall observers with path parameterization in which the non-affinity of the geodesics is equal to the expansion of their velocity vector field. We then provide a proof of the local second law by studying variations in entropy as viewed by this class of covariantly-defined causal free-fall observers. We show that the entropy variation is strictly non-decreasing, provided the matter sector satisfies the integrated strong energy condition along the observer path.
Comments5 pages, two-column, two figures
