THE NERNST THEOREM AND STATISTICAL ENTROPY OF THE SCALAR FIELD IN REISSNER-NORDSTROM GEOMETRY
Reissner-Nordstrom几何中标量场的统计熵与能斯特定理

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.