An improved estimate of black hole entropy in the quantum geometry approach

A proper counting of states for black holes in the quantum geometry approach shows that the dominant configuration for spins are distributions that include spins exceeding one-half at the punctures. This raises the value of the Immirzi parameter and the black hole entropy. However, the coefficient of the logarithmic correction remains -1/2 as before. The quantum geometry approach to a quantum theory of gravity is reasonably well established now: see [1] for reviews. In [2] a general framework for the calculation of black hole entropy in this approach was proposed. A lower bound for the entropy was worked out on the basis of the association of spin one-half to each puncture and found to be proportional to the area of the horizon. The proportionality constant involves what is known as the Immirzi parameter, which can be chosen so that the entropy becomes a quarter of the area. Recently, this lower bound was sharpened in [3] to include a logarithmic correction − 1 2 lnA. Subsequently, it was found [4] that the dominant term in the entropy is somewhat higher by taking spins higher than one-half into account, though the logarithmic correction is unaffected in this calculation. In the present note we investigate the modification of the lower bound of [3] in view of this development and are led to a further increase in the leading term. Let a generic configuration have sj punctures with spin j, j = 1/2, 1, 3/2, 2, .... Note that 2 ∑