Black Holes with Less Entropy Than A/4

Abstract

One can increase one-quarter the area of a black hole, A/4, to exceed the total thermodynamic entropy, S, by surrounding the hole with a perfectly reflecting shell and adiabatically squeezing it inward. A/4 can be made to exceed S by a factor of order unity before the shell enters the Planck regime, though practical limitations are much more restrictive. 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.