A Membrane Paradigm at Large D

We demonstrate that the classical dynamics of black holes simplifies in the large D limit. In this limit we demonstrate a precise `duality' between dynamical black hole solutions and solutions of an auxiliary problem; the motion of a soap bubble type membrane propagating in non dynamical flat space. The dynamical variables of this membrane are its shape and a velocity field. Einstein's equations endow the membrane with a stress tensor, whose form can systematically be determined as a functional of the shape and velocity, order by order in the 1/D expansion. The conservation of this stress tensor yields a well posed initial value problem for the membrane shape and velocity fields, and is the dual description of black hole dynamics at large D. The gravitational radiation that results from any black hole motion is determined from the membrane picture by coupling the membrane stress tensor to gravity. At large D the membrane description can be used to study highly nontrivial black hole solutions, including black hole collisions.

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