On the fundamental length of quantum geometry and the black hole entropy
نویسنده
چکیده
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 lP . 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 √ 3/2( √ γl). 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 BekensteinHawking form. The extremal limit of 1-puncture states of the quantum surface geometry corresponds rather to an extremal string than to a classical horizon. In [1] the black hole entropy for the quantum geometry of the exterior horizon of a black hole has been calculated from first principles. The area is formally proportional to the (real modulus of) the Immirzi[2] parameter γ, parametrizing certain affine transformations of the underlying phase space which maintain the symplectic structure. The result of [1] agrees for one particular value
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