On the fundamental length of quantum geometry and the black hole entropy
Abstract
Description
The geometric operators of area, volume, and length, depend on a fundamental length l of quantum geometry which is a priori arbitrary rather than equal to the Planck length l_P. The fundamental length l and the Immirzi parameter $γ$ determine each other. With any l the entropy formula is rendered most naturally in units of the length gap sqrt{{sqrt 3}/2} (sqrt{gamma} l).
Independently of the choice of l, the black hole entropy derived from quantum geometry in the limit of classical geometry is completely consistent with the Bekenstein-Hawking form.
The extremal limit of 1-puncture states of the quantum surface geometry corresponds rather to an extremal string than to a classical horizon.
4 pages compact revtex format, few sentences straightened
4 pages compact revtex format, few sentences straightened