Hawking-Bekenstein entropy formula seems to tell us that no quantum degrees
of freedom can reside in the interior of a black hole. We suggest that this is
a consequence of the fact that the volume of any interior sphere of finite
surface area simply vanishes. Obviously, this is not the case in general
relativity. However, we show that such a phenomenon does occur in various
gravitational theories which admit a spontaneously induced general relativity.
In such theories, due to a phase transition (one parameter family degenerates)
which takes place precisely at the would have been horizon, the recovered
exterior Schwarzschild solution connects, by means of a self-similar transition
profile, with a novel 'hollow' interior exhibiting a vanishing spatial volume
and a locally varying Newton constant. This constitutes the so-called
'hollowgraphy' driven holography.Comment: Honorable Mention Essay - Gravity Research Foundation (2010
