Wald熵与2+1维引力中的Wen-Zee型规范-曲率耦合
Wald entropy and Wen-Zee type gauge-curvature coupling in 2+1-dimensional gravity
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中文总结 AI 辅助
本文推广Wen-Zee耦合至黑洞时空，证明其Wald熵贡献为视界boost荷，并连接量子霍尔几何响应与引力视界热力学。
中文摘要 AI 辅助
Wen-Zee项是量子霍尔流体拓扑Chern-Simons描述中的一种混合规范-曲率耦合，编码了束缚于空间曲率的电荷。我们研究该耦合的洛伦兹协变推广，将其适用范围扩展到黑洞时空，并确定其对视界熵的贡献。此类耦合自然出现在基于Maxwell代数的三维Chern-Simons引力中。我们证明其Wald熵贡献是一个视界boost荷，由附加规范场沿分叉圆切向投影的环路积分给出。即使混合项在壳上消失，该贡献也可能非零。我们证明当投影方向协变恒定时，该积分具有阿贝尔和乐解释。我们在平坦宇宙学解上评估该荷，并使用光滑视界场和特定热系综，在AdS-Lorentz黑洞上评估该荷。这些结果将量子霍尔物理中熟悉的几何响应与引力视界热力学联系起来。
英文摘要
The Wen-Zee term is a mixed gauge-curvature coupling in the topological Chern-Simons description of a quantum Hall fluid, encoding the electric charge bound to spatial curvature. We investigate a Lorentz-covariant generalisation of this coupling, expanding its scope to black-hole spacetimes and determine its contribution to horizon entropy. Such a coupling arises naturally in three-dimensional Chern-Simons gravity based on the Maxwell algebra. We show that its Wald entropy contribution is a horizon boost charge, given by a loop integral of the additional gauge field projected along the tangent to the bifurcation circle. This contribution can be nonzero even when the mixed term vanishes on shell. We show that the integral admits an Abelian holonomy interpretation when the projection direction is covariantly constant. We evaluate the charge on a flat cosmological solution and, using smooth horizon fields and a specified thermal ensemble, on an AdS-Lorentz black hole. These results connect the geometric response familiar from quantum Hall physics to gravitational horizon thermodynamics.
发表机构
- Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）
- CFisUC, Department of Physics, University of Coimbra（科英布拉大学物理系CFisUC）
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