关于Lovelock引力中de Sitter熵与全息纠缠熵的（不）等价性
On the (In)equivalence of de Sitter and Holographic Entanglement Entropies in Lovelock Gravity
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中文总结 AI 辅助
本文研究高曲率引力中de Sitter熵与全息纠缠熵的关系，证明在RS II膜世界静态时空中两者一致，稳态时不同，并扩展到一般Lovelock引力。
中文摘要 AI 辅助
我们研究了高曲率引力及其膜世界实现中de Sitter熵与全息纠缠熵之间的关系。利用引力作用量的正则形式和欧几里得引力路径积分，我们推导了de Sitter熵，包括高曲率表面项的贡献，并将其与从相应熵泛函获得的全息纠缠熵进行比较。我们首先考虑Gauss-Bonnet引力，并证明在RS II模型上的静态渐近de Sitter膜世界时空中，这两种熵是一致的，而对于稳态时空它们通常不同。稳态情况下的不匹配源于与常时表面相关联的外曲率贡献，该贡献在静态构型中为零，但在稳态几何中通常非零。然后我们将分析扩展到一般Lovelock引力，并证明在RS II模型中，对于静态渐近de Sitter膜世界时空，de Sitter熵与全息纠缠熵之间的一致性在Gauss-Bonnet情形之外仍然成立。我们还评论说，静态与稳态构型之间的相同区别适用于膜世界黑洞：在静态情况下，黑洞熵与全息纠缠熵一致，而对于稳态膜世界黑洞，两者通常不同。我们的结果阐明了高曲率引力中引力熵与全息熵之间的关系，并为Lovelock理论及其膜世界实现中的全息对应提供了更广阔的视角。
英文摘要
We investigate the relation between de Sitter entropy and holographic entanglement entropy in higher-curvature gravity and its braneworld realization. Using the canonical formulation of the gravitational action and the Euclidean gravitational path integral, we derive the de Sitter entropy, including contributions from higher-curvature surface terms, and compare it with the holographic entanglement entropy obtained from the corresponding entropy functional. We first consider Gauss-Bonnet gravity and show that the two entropies coincide for static asymptotically de Sitter braneworld spacetimes on the RS II model, while they generally differ for stationary spacetimes. The mismatch in the stationary case arises from an extrinsic-curvature contribution associated with the constant-time surface, which vanishes for static configurations but is generally nonzero for stationary geometries. We then extend the analysis to general Lovelock gravity and show that the agreement between the de Sitter entropy and holographic entanglement entropy persists for static asymptotically de Sitter braneworld spacetimes in the RS II model beyond the Gauss-Bonnet case. We also comment that the same distinction between static and stationary configurations applies to braneworld black holes: the black hole entropy agrees with the holographic entanglement entropy in the static case, while the two generally differ for stationary braneworld black holes. Our results clarify the relation between gravitational and holographic entropies in higher-curvature gravity and provide a broader perspective on holographic correspondence in Lovelock theories and their braneworld realizations.
发表机构
- National Institute of Technology (KOSEN), Kochi College（国立高等专门学校 Kochi 学院）
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