Fluid/Gravity Correspondence, Local Wald Entropy Current and Gravitational Anomaly

We propose, in the framework of the fluid/gravity correspondence, a definition for a local horizon entropy current for higher-curvature gravitational theories. The current is well-defined to first order in fluid gradients for general gravity actions with an algebraic dependence on the Riemann tensor. As a detailed example, we consider five-dimensional Einstein-Maxwell theory with a mixed gauge-gravitational Chern-Simons term. In this theory, we construct the proposed entropy current on a charged black-brane background, and show that it has a non-negative divergence. Moreover, a complete correspondence between the charged black-brane horizon's dynamics and the hydrodynamics of an anomalous four-dimensional field theory is established. Our proposed entropy current is then found to coincide with the entropy current of the anomalous field theory fluid.