INTEGRABLE DISSIPATIVE STRUCTURES IN THE GAUGE-THEORY OF GRAVITY

The Jackiw-Teitelboim gauge formulation of (1 + 1)-dimensional gravity allows us to relate different gauge-fixing conditions to integrable h ierarchies of evolution equations. We show that the equations for the zweibein fields can be written as a pair of time-reversed evolution eq uations of the reaction-diffusion type, admitting dissipative solution s. The spectral parameter for the related Lax pair appears as the cons tant-valued spin connection associated with the S0(1, 1) gauge symmetr y. Spontaneous breaking of the non-compact symmetry and irreversible e volution are discussed.