Conformal entropy for generalized gravity theories as a consequence of horizon properties

We show that a microscopic entropy formula based on Virasoro algebra follows from properties of stationary Killing horizons for Lagrangians with arbitrary dependence on Riemann tensor. The properties used are a consequence of regularity of invariants of Riemann tensor on the horizon. Eventual generalization of these results to Lagrangians with derivatives of Riemann tensor, as suggested by an example treated in the paper, relies on assuming regularity of invariants involving derivatives of Riemann tensor. This assumption however leads also to new interesting restrictions on metric functions near the horizon.