Quantum geometry and microscopic black hole entropy

Abstract

Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that are consistent with a black hole of a given horizon area $A_0$ are counted and the statistical entropy, as a function of the area, is obtained for $A_0$ up to $550l_{\mathrm{Pl}}^2$. The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to $\gamma =0.274$, which has been previously obtained analytically. However, a new and oscillatory functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation.

10 pages, Revtex4 file, 7 new figures. Discussion expanded, same conclusions

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