类时纠缠熵的度规重构
Metric Reconstruction from Timelike Entanglement Entropy
AI总结：
该研究针对条状类时纠缠熵数据，基于复值弱极值曲面处方开发度规重构方案，可复现基准黑洞黑化因子，但单条状可观测量仅能确定度规函数的一个函数组合。
AI中文摘要：
类时纠缠熵（TEE）提供了体几何的洛伦兹边界探针，但其用于度规重构的过程依赖于全息处方及该处方选定的极值曲面分支。我们针对条状TEE数据研究该逆问题，明确上述依赖关系。在复值弱极值曲面（CWES）处方中，TEE的时间宽度依赖关系在选定的实分支上确定了阿贝尔密度H(W)；对于Bañados-Teitelboim-Zanelli（BTZ）黑洞，一旦奇点端点固定径向原点，该密度可解析重构黑化因子。在开发了复坐标处方的正向数值方法后，我们将其表述为d≥2的渐近AdS_{d+1}背景的主要重构方案。在选定的复分支上，TEE的时间宽度依赖关系提供了确定TEE可及密度的阿贝尔输入，同时需要一个额外的几何锚点将该密度转换为确定的径向度规轮廓。结合UV或视界尺度锚点以及从重构的复路径样本进行的有理延拓，该方法可复现基准BTZ、四维史瓦西及Reissner-Nordström（RN）黑化因子。但Gubser-Rocha示例表明，具有非平凡空间扭曲因子的单个条状可观测量仅能确定度规函数的一个函数组合。
英文摘要：
Timelike entanglement entropy (TEE) provides a Lorentzian boundary probe of bulk geometry, but its use for metric reconstruction depends on the holographic prescription and on the extremal-surface branch selected by that prescription. We study this inverse problem for strip-shaped TEE data and make these dependencies explicit. In the complex-valued weak extremal surface (CWES) prescription, the time-width dependence of TEE determines an Abel density $H(W)$ on a selected real branch; for Bañados-Teitelboim-Zanelli (BTZ) black holes this gives an analytic reconstruction of the blackening factor once the singularity endpoint fixes the radial origin. After developing a forward numerical method for the complex-coordinate prescription, we formulate it as the main reconstruction scheme for the asymptotically $AdS_{d+1}$ backgrounds with $d\geq 2$. On a chosen complex branch, the time-width dependence of TEE supplies the Abel input that determines the TEE-accessible density, while one additional geometric anchor is required to convert that density into a definite radial metric profile. With UV or horizon-scale anchoring and rational continuation from the reconstructed complex-path samples, the method reproduces the benchmark BTZ, four-dimensional Schwarzschild, and Reissner-Nordström (RN) blackening factors. However, the Gubser-Rocha example shows that a single strip observable with a nontrivial spatial warp factor determines only one functional combination of the metric functions.
