发表机构
Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过全息探针（CV、CA、HM熵和热a-函数）对平面AdS黑洞内部的Kasner指数施加代数约束，并证明经典能量条件（零和主能量条件）是这些约束的充分条件，建立了体能量条件与内部几何的直接联系。
AI 中文摘要
自下而上全息理论中的一个核心问题是，给定的体有效理论是否允许存在一致的全息对偶。在本工作中，我们探讨了平面AdS黑洞内部的近奇点Kasner标度是否可以作为基于内部敏感全息探针的有用诊断工具。通过检查控制内部敏感可观测量的度规组合，包括复杂度=体积（CV）、复杂度=作用量（CA）的体贡献、Hartman-Maldacena（HM）熵以及热$a$-函数，我们推导了在相关半经典区域中Kasner指数$(p_t,p_s)$的代数界限：CV和HM的有限半径晚期分支、有限的CA复杂度以及有限的近奇点热$a$-函数。由此产生的不等式描绘了Kasner空间中相应的区域，在这些区域中，仅终端标度就足以实现这些行为。此外，我们证明了经典能量条件，特别是零能量条件和主能量条件，提供了简单的充分准则，确保Kasner指数落在这些全息允许的区域内。这些结果建立了经典体能量条件与全息探针所选择的内部几何之间的直接联系，并表明Kasner标度可以为自下而上的全息理论提供补充诊断。
英文摘要
A central question in bottom-up holography is whether a given bulk effective theory admits a consistent holographic dual. In this work, we explore whether the near-singularity Kasner scaling of planar AdS black hole interiors can serve as a useful diagnostic based on interior-sensitive holographic probes. By examining the metric combinations that control interior-sensitive observables, including Complexity=Volume (CV), the bulk contribution to Complexity=Action (CA), Hartman-Maldacena (HM) entropy, and the thermal $a$-function, we derive algebraic bounds on the Kasner exponents $(p_t,p_s)$ for the relevant semi-classical regimes: finite-radius late-time branches of CV and HM, finite CA complexity, and a finite near-singularity thermal $a$-function. The resulting inequalities delineate the corresponding regions of Kasner space in which the terminal scaling alone is sufficient to realize these behaviors. Furthermore, we demonstrate that classical energy conditions, specifically the null and dominant energy conditions, provide simple sufficient criteria ensuring that the Kasner exponents fall within these holographically allowed regions. These results establish a direct connection between classical bulk energy conditions and the interior geometry selected by holographic probes, and suggest that Kasner scaling can provide a complementary diagnostic in bottom-up holography.
Comments33 pages, 7 figures; v2: added new references
