Hall Scrambling on Black Hole Horizons

We 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, we show that in the presence of the $\theta$-term, a black hole horizon behaves as a Hall conductor, for an observer hovering outside. We study how localized perturbations created on the stretched horizon scramble on the horizon by dropping a charged particle. We show that the $\theta$-angle affects the way perturbations scramble on the horizon, in particular, it introduces vortices without changing the scrambling time. This Hall scrambling of information is also expected to occur on cosmological horizons.