On the fundamental length of quantum geometry and the black hole entropy

Details On the fundamental length of quantum geometry and the black hole entropy On the fundamental length of quantum geometry and the black hole entropy

1999-03-24

arxiv.org/abs/gr-qc/9903091v3

Grav.Cosmol. 6 (2000) 181-184

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages compact revtex format, few sentences straightened

Scientific paper

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 $\gamma$ 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.

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