论文标题
标量和量规场与重力的非最小耦合：熵电流和线性第二定律
Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law
论文作者
论文摘要
这项工作扩展了线性化第二法的本地版本的证明，该法律涉及具有非负分歧的熵电流，其中包括标量的任意非微耦合和$ u（1）$ u（1）$ gauge gravility。在最近的工作中，熵电流的构建以证明线性化的第二定律基于对重力的可能物质耦合的重要假设：假定相应的物质应力张量可以满足无效的能量条件。但是，当考虑物质场与重力的非最小耦合时，也可以在经典上违反无效的能量条件。考虑到在固定的黑洞周围的小小动力扰动中，在差异性重力理论中具有非微耦合与标量或量规场的非最小耦合，我们证明仍然可以构建具有非负差异的熵电流。我们已纳入的其他非最小耦合有助于熵电流，甚至可能在平衡极限内生存。除了平衡情况下的熵密度外，我们还获得了地平线上的空间电流。我们通过使用近距地平线几何形状的增强对称性来实现这一目标，该几何形状限制了运动方程的特定组件的外壳结构，并以较新的术语来限制非最小耦合。熵电流的最终表达式为$ u（1）$ g量规数，用于量规场与重力。我们明确检查是否从我们的抽象参数获得的熵电流与文献中已经可用的表达式相一致，这些特定模型理论涉及物质与更高衍生的重力理论的非微耦合。最后，我们还认为，第一定律的物理过程版本与任意非最小物质耦合有关这些理论。
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.
