Integrable dissipative structures in the gauge theory of gravity

Abstract

The Jackiw-Teitelboim gauge formulation of the 1+1 dimensional gravity allows us to relate different gauge fixing conditions with integrable hierarchies of evolution equations. We show that the equations for the Zweibein fields can be written as a pair of time reversed evolution equations of the reaction-diffusion type, admitting dissipative solutions. The spectral parameter for the related Lax pair appears as the constant valued spin connection associated with the $SO(1,1)$ gauge symmetry. Spontaneous breaking of the non-compact symmetry and the irreversible evolution are discussed.

12 pages, Latex, no figures, to appear in Class. Quantum. Grav

Cited by in corpus (9)

• Resonance NLS Solitons as Black Holes in Madelung Fluid
• Degenerate Four Virtual Soliton Resonance for KP-II
• Soliton Resonances for MKP-II
• Equations of the reaction-diffusion type with a loop algebra structure
• Moving Frames Hierarchy and BF Theory
• Fifth-order generalized Heisenberg supermagnetic models
• Chern-Simons Solitons in Quantum Potential
• Algebraic structures generating reaction-diffusion models: the activator-substrate system
• Self-Dual Vortices in Chern-Simons Hydrodynamics