PERTURBATIVE METHOD TO SOLVE 4TH-ORDER GRAVITY-FIELD EQUATIONS

We develop a method for solving the field equations of a quadratic gra vitational theory coupled to matter. The quadratic terms are written a s a function of the matter stress tensor and its derivatives in such a way as to have, order by order, a set of Einstein field equations wit h an effective T(munu). We study the cosmological scenario recovering the de Sitter exact solution, and the first order (in the coupling con stants alpha and beta appearing in the gravitational Lagrangian) solut ion to the gauge cosmic string metric and the charged black hole. For this last solution we discuss the consequences on the thermodynamics o f black holes, and, in particular, the entropy-area relation which get s additional terms to the usual A/4 value.