  We study a black hole of mass $M$, enclosed within a spherical box, in
equilibrium with its Hawking radiation. We show that the spacetime geometry
inside the box is described by the Oppenheimer-Volkoff equations for radiation,
except for a {\em thin shell} around the horizon. We use the maximum entropy
principle to show that the invariant width of the shell is of order $\sqrt{M}$,
its entropy is of order $M$ and its temperature of order $1/\sqrt{M}$ (in
Planck units). Thus, the width of the shell is {\em much larger} than the
Planck length. Our approach is to insist on thermodynamic consistency when
classical general relativity coexists with the Hawking temperature in the
description of a gravitating system. No assumptions about an underlying theory
are made and no restrictions are placed on the origins of the new physics near
the horizon. We only employ classical general relativity and the principles of
thermodynamics. Our result is strengthened by an analysis of the trace anomaly
associated to the geometry inside the box, i.e., the regime where quantum field
effects become significant corresponds to the shells of maximum entropy around
the horizon.
