QUASI-LOCAL THERMODYNAMICS OF DILATON GRAVITY COUPLED TO GAUGE-FIELDS

We consider an Einstein-Hilbert-dilaton action for gravity coupled to various types of Abelian and non-Abelian gauge fields in a spatially f inite system. These include Yang-Mills fields and Abelian gauge fields with three-form and four-form field strengths. We obtain various quas ilocal quantities associated with these fields, including their energy and angular momentum, and develop methods for calculating conserved c harges when a solution possesses sufficient symmetry. For stationary b lack holes, we find an expression for the entropy from the microcanoni cal form of the action. We also find a form of the first law of black hole thermodynamics for black holes with the gauge fields of the type considered here.