德西特时空的类时全息复杂度
Holographic timelike complexity for de Sitter
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中文总结 AI 辅助
本文在德西特时空静态补丁全息框架下，利用拉伸视界规定计算纯德西特与施瓦西-德西特时空的类时子区域全息复杂度及对应纠缠熵，分析其增长特性并与类空复杂度对比。
中文摘要 AI 辅助
我们在德西特时空的静态补丁全息框架下，研究了近期提出的类时子区域的全息体积复杂度方案[Alishahiha:2025xml]。利用拉伸视界规定，我们针对纯德西特和施瓦西-德西特几何，计算了类时子区域复杂度随子区域时长的变化关系。在纯德西特时空中，类时子区域复杂度在短时长呈现指数增长，在接近最大时长时呈超快速增长，这与类空体积复杂度的特征[Jorstad:2022mls]类似。对于施瓦西-德西特时空，当拉伸视界靠近宇宙学视界时，其行为与纯德西特时空大致相似；但当拉伸视界靠近黑洞视界时，长时长下的超快速增长被非线性增长 regime 取代。在此过程中，我们还计算了德西特和施瓦西-德西特对应的类时全息纠缠熵。
英文摘要
We investigate the recent proposal of holographic volume complexity for timelike subregions \cite{Alishahiha:2025xml} in the framework of static patch holography for de Sitter spacetime. Using the stretched-horizon prescription, we compute the timelike subregion complexity as a function of the subregion duration for pure de Sitter and Schwarzschild de Sitter geometries. In pure de Sitter spacetime, the timelike subregion complexity displays exponential growth for short durations, and hyperfast growth near a maximal duration, paralleling the features of spacelike volume complexity \cite{Jorstad:2022mls}. For Schwarzschild de Sitter, when the stretched horizon is near the cosmological horizon, the behavior broadly remains similar to pure de Sitter. However, when the stretched horizon is near the black hole horizon, the hyperfast growth for long durations is replaced by nonlinear growth regime. Along the way, we also compute the corresponding timelike holographic entanglement entropy for de Sitter and Schwarzschild de Sitter.
