Abstract
Two-dimensional Poincare gauge gravity is known to be completely integrable in vacuum. Interaction with matter fields usually destroys the integrability. We give a coordinate- and gauge-invariant formulation of the matter-gravity dynamics for the general quadratic Poincare gauge model. The particular cases of massless spinor and scalar field sources are analyzed in detail. Exact general solutions for the chiral boson and fermion matter field configurations are constructed. These describe the gravitational field of a black hole type and are similar to the vacuum solutions discovered earlier. Nonchiral solutions are investigated with the help of numerical methods.
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