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arXiv · 2104.09676

Integrable Systems and Spacetime Dynamics

Marcela Cárdenas·Francisco Correa·Kristiansen Lara·Miguel Pino
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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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Marcela Cárdenas, Francisco Correa, Kristiansen Lara, Miguel Pino. 2021-10-13. Integrable Systems and Spacetime Dynamics. https://doi.org/10.1103/physrevlett.127.161601

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