标题： 标量场和规范场与引力的非最小耦合：熵流和线性化第二定律 显示英文标题

标题： Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law

摘要： 这项工作扩展了关于包含具有非负散度的熵流的线性化第二定律局部版本的证明，通过包括标量和$U(1)$规范场与引力的任意非最小耦合。 在最近的研究中，构建熵流以证明线性化第二定律依赖于一个关于物质与引力可能耦合的重要假设：对应的物质应力张量被假定满足零能量条件。 然而，当考虑物质场与引力的非最小耦合时，零能量条件甚至可以在经典情况下被违反。 考虑到在具有非最小耦合到标量或规范场的引力微分同胚不变理论中，围绕静态黑洞的小动态扰动，我们证明仍然可以构建具有非负散度的熵流。 我们所纳入的额外非最小耦合对熵流有所贡献，这甚至可能在平衡极限下仍然存在。 除了非平衡情况下的熵密度外，我们在视界上还得到了一个空间流。 我们通过利用近视界几何的提升对称性来实现这一点，该对称性约束了由于非最小耦合而出现的新项的特定运动方程的非壳结构。 熵流的最终表达式对于与引力耦合的$U(1)$规范场是规范不变的。 我们明确检查了从我们的抽象论证中得到的熵流与文献中已有的一些涉及物质与高阶导数引力理论非最小耦合的具体模型理论的表达式是一致的。 最后，我们也认为，这些具有任意非最小物质耦合的理论的第一定律的物理过程版本是成立的。 显示英文摘要

摘要： This work extends the proof of a local version of the linearized second law involving an entropy current with non-negative divergence by including the arbitrary non-minimal coupling of scalar and $U(1)$ gauge fields with gravity. In recent works, the construction of entropy current to prove the linearized second law rested on an important assumption about the possible matter couplings to gravity: the corresponding matter stress tensor was assumed to satisfy the null energy conditions. However, the null energy condition can be violated, even classically, when the non-minimal coupling of matter fields to gravity is considered. Considering small dynamical perturbations around stationary black holes in diffeomorphism invariant theories of gravity with non-minimal coupling to scalar or gauge fields, we prove that an entropy current with non-negative divergence can still be constructed. The additional non-minimal couplings that we have incorporated contribute to the entropy current, which may even survive in the equilibrium limit. We also obtain a spatial current on the horizon apart from the entropy density in out-of-equilibrium situations. We achieve this by using a boost symmetry of the near horizon geometry, which constraints the off-shell structure of a specific component of the equations of motion with newer terms due to the non-minimal couplings. The final expression for the entropy current is $U(1)$ gauge-invariant for gauge fields coupled to gravity. We explicitly check that the entropy current obtained from our abstract arguments is consistent with the expressions already available in the literature for specific model theories involving non-minimal coupling of matter with higher derivative theories of gravity. Finally, we also argue that the physical process version of the first law holds for these theories with arbitrary non-minimal matter couplings.