Integrable Systems and Spacetime Dynamics

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.

arXiv comment5 pages. Replacement matches with published version

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Cited by in corpus (8)

• Negative flows of generalized KdV and mKdV hierarchies and their gauge-Miura transformations
• Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields
• KdV conformal symmetry breaking in nearly AdS${}_2$
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy
• DC conductance and memory in 3D gravity
• AdS${}_3$ Carroll gravity: asymptotic symmetries and C-thermal configurations
• On the Explicit Asymptotic Symmetry Breaking of sl(3,R) Jackiw-Teitelboim Gravity
• Integrability of Three Dimensional Gravity Field Equations