Non-Boltzmann Statistics as an Alternative to Holography

Abstract

An intriguing question related to black hole thermodynamics is that the entropy of a region shall scale as the area rather than the volume. In this essay we propose that the microscopical degrees of freedom contained in a given region of space, are statistically related in such a way that obey a non-standard statistics, in which case an holographic hypothesis would be not needed. This could provide us with some insight about the nature of degrees of freedom of the geometry and/or the way in which gravitation plays a role in the statistic correlation between the degrees of freedom of a system.

Presented in the 2005 Essay Competition of the Gravity Research Foundation. To appear in Int. Jour. of Mod. Phys. A