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Integrable dissipative structures in the gauge theory of gravity

L. Martina·O. K. Pashaev·G. Soliani
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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.

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L. Martina, O. K. Pashaev, G. Soliani. 1997-10-17. Integrable dissipative structures in the gauge theory of gravity. https://doi.org/10.1088/0264-9381%2F14%2F12%2F005

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