Generalized uncertainty principle and entropy of three-dimensional BTZ black hole

Abstract

Applying the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity field，we investigate the black hole entropy on the background of three-dimensionnal BTZ. When the λ with the Planck scale，and relative to the dimensions of spacetime introduced in generalized uncertainty relation has a fixed value，we obtain the Bekenstein-Hawking entropy of BTZ black hole and the correction term. Because we have used the new equation of state density，in our results the divergence term appearing in the brick-wall model is removed，at the same time with holding the small mass approximation. Thus the correction value of the Bekenstein-Hawking entropy of the black hole is derived from the quantum statistical view. It depends the understanding of the correction value of the black hole entropy.