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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 √(TT̅) 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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Cite

BibTeXRIS
BibTeX
@misc{adami2026integrable,
  title = {{On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity}},
  author = {Hamed Adami and Kristiansen Lara and Anouchah Latifi and René Meyer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.06867},
  eprint = {2607.06867},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.06867},
}
RIS
TY  - UNPB
TI  - On Integrable Structures on Non-compact Boundaries in Three-Dimensional Gravity
AU  - Hamed Adami
AU  - Kristiansen Lara
AU  - Anouchah Latifi
AU  - René Meyer
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2607.06867
UR  - https://arxiv.org/abs/2607.06867
AB  - 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 √(TT̅) 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.
ER  -