Effective Theories of Horizons - III

The classical dynamics of space times with event horizons is often of great interest - but in general is very complicated. We will demonstrate that event horizon dynamics simplifies in the limit of a large number of dimensions. In this limit event horizon dynamics is governed by the equations of a dynamical membrane that hosts a velocity and charge density field. At leading order in the large D expansion we determine the effective equations of membrane dynamics. We discuss possible applications of our construction.