The gravitational field of a black hole is strongly localized near its
horizon when the number of dimensions D is very large. In this limit, we can
effectively replace the black hole with a surface in a background geometry (eg
Minkowski or Anti-deSitter space). The Einstein equations determine the
effective equations that this 'black hole surface' (or membrane) must satisfy.
We obtain them up to next-to-leading order in 1/D for static black holes of the
Einstein-(A)dS theory. To leading order, and also to next order in Minkowski
backgrounds, the equations of the effective theory are the same as soap-film
equations, possibly up to a redshift factor. In particular, the Schwarzschild
black hole is recovered as a spherical soap bubble. Less trivially, we find
solutions for 'black droplets', ie black holes localized at the boundary of
AdS, and for non-uniform black strings.Comment: 32 pages, 3 figure
