Quantum Statistic Entropy of Three-Dimensional BTZ Black Hole

Using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity, we investigate entropy of a black line on the background of the three-dimensional BTZ. In our calculation, we need not introduce cutoff and can remove the divergent term in the original brick-wall method via the new equation of state density. And it is obtained that the entropy of the black line is proportional to the area of the horizon (perimeter). Further it is shown the entropy of black line is the entropy of quantum state on the surface of horizon (perimeter). The black line entropy is the intrinsic property of the black hole. The entropy is a quantum effect. By using quantum statistical method, we directly obtain the partition function of Bose field and fermi field on the background of the black line. The difficulty to solve wave equation of various particles is avoided. We offer a new simple and direct way for calculating the entropy of various spacetime black holes (black plane, black line and black column). PACS 04.20.Dw; 97.60.Lf