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We study a black hole of mass $M$, enclosed within a spherical box, inequilibrium with its Hawking radiation. We show that the spacetime geometryinside the box is described by the Oppenheimer-Volkoff equations for radiation,except for a {\em thin shell} around the horizon. We use the maximum entropyprinciple 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 $1/\sqrt{M}$ (inPlanck units). Thus, the width of the shell is {\em much larger} than thePlanck length. Our approach is to insist on thermodynamic consistency whenclassical general relativity coexists with the Hawking temperature in thedescription of a gravitating system. No assumptions about an underlying theoryare made and no restrictions are placed on the origins of the new physics nearthe horizon. We only employ classical general relativity and the principles ofthermodynamics. Our result is strengthened by an analysis of the trace anomalyassociated to the geometry inside the box, i.e., the regime where quantum fieldeffects become significant corresponds to the shells of maximum entropy aroundthe horizon.

The thermodynamics of a black hole in equilibrium implies the breakdown of Einstein equations on a macroscopic near-horizon shell