Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes

Oscar Fuentealba, Javier Matulich, Alfredo Pérez, Miguel Pino, Pablo Rodríguez, David Tempo*, Ricardo Troncoso

*Autor correspondiente de este trabajo

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

27 Citas (Scopus)

Resumen

We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS3 algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis is performed in terms of two-dimensional gauge fields for isl(2 ℝ) , being isomorphic to the Poincaré algebra in 3D. Although the algebra is not semisimple, the formulation can still be carried out à la Drinfeld-Sokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be bi-Hamiltonian, labeled by a nonnegative integer k, and defined through a suitable generalization of the Gelfand-Dikii polynomials. The symmetries of the hierarchy are explicitly found. For k ≥ 1, the corresponding conserved charges span an infinite-dimensional Abelian algebra without central extensions, so that they are in involution; while in the case of k = 0, they generate the BMS3 algebra. In the special case of k = 1, by virtue of a suitable field redefinition and time scaling, the field equations are shown to be equivalent to the ones of a specific type of the Hirota-Satsuma coupled KdV systems. For k ≥ 1, the hierarchy also includes the so-called perturbed KdV equations as a particular case. A wide class of analytic solutions is also explicitly constructed for a generic value of k. Remarkably, the dynamics can be fully geometrized so as to describe the evolution of spacelike surfaces embedded in locally flat spacetimes. Indeed, General Relativity in 3D can be endowed with a suitable set of boundary conditions, so that the Einstein equations precisely reduce to the ones of the hierarchy aforementioned. The symmetries of the integrable systems then arise as diffeomorphisms that preserve the asymptotic form of the spacetime metric, and therefore, they become Noetherian. The infinite set of conserved charges is then recovered from the corresponding surface integrals in the canonical approach.

Idioma originalInglés
Número de artículo148
PublicaciónJournal of High Energy Physics
Volumen2018
N.º1
DOI
EstadoPublicada - 2018
Publicado de forma externa

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Publisher Copyright:
© 2018, The Author(s).

Áreas temáticas de ASJC Scopus

  • Física nuclear y de alta energía

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