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arXiv · 2607.06867

On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity

Hamed Adami·Kristiansen Lara·Anouchah Latifi·René Meyer
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Abstract

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 $T\bar T$ 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.

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Hamed Adami, Kristiansen Lara, Anouchah Latifi, René Meyer. 2026-07-07. On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity. https://arxiv.org/abs/2607.06867

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