Holographic effective actions from black holes

Using the Waldʼs relation between the Noether charge of diffeomorphisms and the entropy for a generic spacetime possessing a bifurcation surface, we introduce a method to obtain a family of higher order derivatives effective actions from the entropy of black holes. We consider the entropy as the starting point and we analyze the procedure of derivation of the action functional. We specialize to a particular class of theories which simplifies the calculations, f(R) theories. We apply the procedure to loop quantum gravity and to a general class of log-corrected entropy formulas.