Black Hole Configurations with Total Entropy Less than A/4

If one surrounds a black hole with a perfectly reflecting shell and adiabatically squeezes the shell inward, one can increase the black hole area A to exceed four times the total entropy S, which stays fixed during the process. A can be made to exceed 4S by a factor of order unity before the one enters the Planck regime where the semiclassical approximation breaks down. One interpretation is that the black hole entropy resides in its thermal atmosphere, and the shell restricts the atmosphere so that its entropy is less than A/4.