Reissner-Nordstrom几何中标量场的统计熵与能斯特定理

从Reissner-Nordstrom时空背景下的Klein-Gordon方程出发,利用改进的brick-wall方法膜模型,计算黑洞背景下标量场的自由能和熵.得到标量场的熵是由两部分组成的,根据熵是广延量的性质,得到黑洞熵是由两个子热力学系统贡献的.在此基础上给出了新的Bekenstein-Smarr公式.结果表明,用两个子热力学系统表达的熵,当黑洞的辐射温度趋于绝对零度时,黑洞的熵也趋于零,它满足能斯特定理,可视为黑洞的普朗克绝对熵.关键词：brick-wall方法膜模型黑洞熵能斯特定理

THE NERNST THEOREM AND STATISTICAL ENTROPY OF THE SCALAR FIELD IN REISSNER-NORDSTROM GEOMETRY

Based on the Klein-Gordon equations on the background of the Reisser-Nordstrom spacetime, we calculate the free energy and entropy of a scalar field near a black hole by improved brick-wall methodmembrane model. It is obtained that the entropy of the scalar field consists of two parts. As the entropy is an extensive quantity, we obtain that the black hole entropy comes from two thermodynamical systems. And the new Bekenstein-Smarr formula is given. It is shown that the entropy expressed by two thermodynamical subsystems approaches zero when the radiation temperature of the black hole approaches absolute zero. This obeys Nernst theorem. It can be taken as Planck absolute entropy of a black hole.