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 finite system. These include Yang-Mills fields and Abelian gauge fields with three-form and four-form field strengths. We obtain various quasilocal quantities associated with these fields, including their energy and angular momentum, and develop methods for calculating conserved charges when a solution possesses sufficient symmetry. For stationary black holes, we find an expression for the entropy from the microcanonical 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.