Horizon tunneling revisited: the case of higher dimensional black holes

We study the tunneling of massless scalars across black hole horizons in any number of spacetime dimensions greater than three. Our analysis fi nds that corrections due to backreaction and the inverse dimensional expansion are naturally concomitant, and furnishes a simple proof of the classic relation between entropy and area in all spacetime dimensions, fi nite or in fi nite. We conclude with a discussion of the limit in which the number of spacetime dimensions is taken to in fi nity, where we fi nd that thermodynamic quantities are related to the "thickness" of the membrane on which all the curvature is localized.