Membrane paradigm, total derivative terms and gauge/gravity duality

First, I explore the effect of the electrodynamics theta-angle on the macroscopic properties of black hole horizons. Using only classical Einstein-Maxwell-Chern-Simons theory in (3+1)-dimensions, in the form of the membrane paradigm, I show that in the presence of the theta-term, a black hole horizon behaves as a Hall conductor, for an observer hovering outside. I will show how localized perturbations created on the stretched horizon scramble on the horizon by dropping a charged particle. The theta-angle affects the way perturbations scramble on the horizon, in particular, it introduces vortices without changing the scrambling time. Then I will explore the effect of similar gravity terms on the behavior of the stretched horizon of a black hole. Finally, I will show the relation between these effects on the stretched horizon of a black hole in (3+1)-dimensional AdS spacetime and the dual gauge theory.