Black Hole Entropy in the Presence of Chern–Simons Term and Holography

We propose a manifestly covariant formulation of the differential Noether charge for higher-dimensional Chern–Simons terms. With our differential Noether charge, we provide a covariant proof of the black hole entropy formula for gravitational and mixed U(1)-gravitational Chern–Simons terms. By evaluating the charge on the rotating charged AdS black hole background constructed by the fluid/gravity derivative expansion, we show that the Chern–Simons contribution to black hole entropy agrees with the anomaly-induced entropy current in the dual conformal field theory at the leading order of the derivative expansion.