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Integrable Systems and Spacetime Dynamics

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arxiv 2104.09676 v3 pith:UN75QXL5 submitted 2021-04-19 hep-th gr-qcnlin.SI

Marcela Cárdenas , Francisco Correa , Kristiansen Lara , Miguel Pino This is my paper · ORCID
classification hep-thgr-qcnlin.SI
keywords aknsboundaryconditionsgravitationalintegrableablowitz-kaup-newell-segurasymptoticblack
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abstract

It is shown that the Ablowitz-Kaup-Newell-Segur (AKNS) integrable hierarchy can be obtained as the dynamical equations of three-dimensional General Relativity with a negative cosmological constant. This geometrization of the AKNS system is possible through the construction of novel boundary conditions for the gravitational field. These are invariant under an asymptotic symmetry group characterized by an infinite set of AKNS commuting conserved charges. Gravitational configurations are studied by means of $SL(2,\mathbb{R})$ conjugacy classes. Conical singularities and black hole solutions are included in the boundary conditions.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    hep-th 2026-07 conditional novelty 6.0 of 10

    In the diagonal (Cartan) sector of AdS3 gravity, the radial flow of the quasi-local stress tensor satisfies an exact T Tbar-like equation, while the boundary time evolution forms an integrable bi-Hamiltonian hierarchy.

  2. Generalized Fefferman-Graham gauge and boundary Weyl structures

    hep-th 2024-11 conditional novelty 6.0 of 10

    In the generalized Fefferman-Graham gauge, three-dimensional AdS gravity produces a boundary Weyl connection, a Weyl-covariant stress tensor and trace anomaly, and requires a new corner counterterm that fixes the Eucl...

  3. Generalized Schwarzian Dynamics from a Bulk-First BF Perspective

    hep-th 2026-06 unverdicted novelty 5.5 of 10

    The sl(3,R) BF reduction is re-expressed through Wilczynski invariants, yielding a generalized Schwarzian action and a heuristic thermodynamic dictionary to Casimir and monodromy data.

  4. Integrable black hole dynamics in the asymptotic structure of AdS$_{3}$

    hep-th 2025-04 conditional novelty 5.0 of 10

    In AdS3, a relaxed class of boundary conditions makes Einstein's equations reduce to two AKNS integrable hierarchies, and stationary black holes in this class have constant temperatures fixed by hyperelliptic spectra,...

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