Fractal black holes and information

Abstract

If nature is fractal as it evidently is, at classical resolution and if it is suspected to also be fractal at the quantum resolution as it is now a days generally believed to be, then we must have over looked at least two points or so in our physical model building of mini black holes. To start with at such ultra high resolution, the mini black hole geometry must be a fractal. Consequently we have zero volume and only a fractal surface area. Second because we cannot take the differential limit for the ℓp2 covering the transfinite surface area, there will be many gaps between the (ℓp)2 tilings. In other words we must introduce transfinite corrections to the final result. Proceeding this way the information entropy unit of a black hole should bea=I=(7+ϕ3)(10)-66cm2=7.23606799(10)-66cm2The nearest classical result to the above is that obtained by Gerard ‘t Hoofta=I=(0.724)(10)-65cm2The paper ends with a general discussion of E-infinity theory and its possible relation with ‘t Hooft’s holographic principle and his gluons–quark strings.