发表机构
Fudan University; Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS); Centro de Estudios Científicos (CECs); Facultad de Ingeniería, Universidad San Sebastián; Qom University of Technology; Julius-Maximilians-Universität Würzburg（复旦大学; 上海数学与交叉学科研究院; 科学研究中心; 圣塞巴斯蒂安大学工程学院; 库姆理工大学; 维尔茨堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究三维爱因斯坦引力在非紧致边界情况，利用流体/引力对应推导径向流方程实现全息$T\bar T$形变，发展逆散射描述，虽边界演化由可积双哈密顿层次控制，但径向流非哈密顿，建立相关统一框架。
AI 中文摘要
我们在陈 - 西蒙斯形式体系内研究具有负宇宙学常数的三维爱因斯坦引力在非紧致空间边界的情况。利用精确的流体/引力对应关系，我们推导了准局部应力张量的封闭径向流方程，并表明它在有限截断下实现了全息$T\bar T$形变。我们进一步发展了边界动力学的逆散射描述，确定了相关谱数据的引力解释并分析了孤子解的有限截断形变。虽然边界演化由可积双哈密顿层次结构控制，但径向流本身相对于正则泊松结构不是哈密顿的。我们的结果建立了一个统一框架，连接了非紧致边界上的可积性、准局部引力可观测量、逆散射和有限截断全息术。
英文摘要
We study three-dimensional Einstein gravity with negative cosmological constant on non-compact spatial boundaries within the Chern-Simons formulation. Using an exact fluid/gravity correspondence, we derive a closed radial flow equation for the quasi-local stress tensor and show that it realizes the holographic $\sqrt{T\bar T}$ deformation at finite cutoff. We further develop the inverse-scattering description of the boundary dynamics, identifying the gravitational interpretation of the associated spectral data and analyzing the finite-cutoff deformation of soliton solutions. Although the boundary evolution is governed by an integrable bi-Hamiltonian hierarchy, we show that the radial flow itself is not Hamiltonian with respect to the canonical Poisson structure. Our results establish a unified framework connecting integrability, quasi-local gravitational observables, inverse scattering, and finite-cutoff holography on non-compact boundaries.
Comments26 pages. Minor clarifications and typographical corrections. The main results are unchanged
