Entropy current for higher derivative theories of gravity

We know that black holes could be viewed as thermodynamic ensemble of large number of microstates and therefore we could associate some entropy with these objects. For Einstein gravity, the local area element around any point of the black hole horizon plays the role of entropy density, that satisfies the second law of thermodynamics locally at every point on the horizon. However, any UV complete theory of gravity, in its low energy limit, will typically have higher derivative corrections to Einstein gravity. Black holes continue to exist for such higher derivative theories. In this talk, we shall show that for such theories we could still satisfy the second law locally on every point of the horizon, at least when the dynamics of the black hole is of small amplitude. To see this, we need to add a spatial entropy current to the equilibrium construction of Wald entropy density. This method also fixes some of the ambiguities that arise in Wald’s construction, for the entropy of a dynamical black hole in higher derivative theories.