广义测不准关系与三维BTZ黑洞熵

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

通过应用在量子引力中,由广义测不准关系得出的新的态密度方程,研究三维BTZ背景下黑洞的熵.当取广义测不准关系中引入的,具有Planck量级与空间维数有关的常数λ为特定值时,得到BTZ黑洞Bekenstein-Hawking熵和修正项.由于利用新的态密度方程,在计算中不存在用brick-wall模型计算黑洞熵时出现的发散项和小质量近似.所得结论,从量子统计力学角度给出了黑洞Bekenstein-Hawking熵的修正值,使人们对黑洞熵的修正值有更深入的认识.

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.