A Charged Membrane Paradigm at Large D

Understand

We study the effective dynamics of black hole horizons in Einstein-Maxwell theory in a large number of spacetime dimensions $D$.

• We demonstrate that horizon dynamics may be recast as a well posed initial value problem for the motion of a codimension one non gravitational membrane moving in flat space.
• The dynamical degrees of freedom of this membrane are its shape, charge density and a divergence free velocity field.
• We determine the equations that govern membrane dynamics at leading order in the large $D$ expansion.