Hollowgraphy Driven Holography: Black Hole with Vanishing Volume Interior

Abstract: 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.