Integrable Systems and Spacetime Dynamics

Open Access

Integrable Systems and Spacetime Dynamics

Marcela Cárdenas, Francisco Correa, Kristiansen Lara, and Miguel Pino

Phys. Rev. Lett. 127, 161601 – Published 12 October 2021

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 $S L (2, R)$ conjugacy classes. Conical singularities and black hole solutions are included in the boundary conditions.

Received 31 May 2021
Accepted 21 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.161601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Gauge-gravity dualities

Infinite-dimensional symmetries

Integrable systems

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Marcela Cárdenas^1,*, Francisco Correa ^2,†, Kristiansen Lara ^1,‡, and Miguel Pino ^1,3,§

¹Departamento de Física, Universidad de Santiago de Chile, Avenida Ecuador 3493, Estación Central, 9170124 Santiago, Chile
²Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia, Chile
³Center for Interdisciplinary Research in Astrophysics and Space Exploration (CIRAS), Universidad de Santiago de Chile, Avenida Libertador Bernardo O’Higgins, 3363 Estación Central, Chile