THE NERNST THEOREM AND THE ENTROPY OF A CYLINDRICAL BLACK HOLE

Under nonspherical coordinates, the free energy and the entropy of a scalar field are calculated in terms of the brick-wall method on the background of a nonasymptotically flat cylindrical black hole. It is shown that the entropy is not only related to the area of an outer horizon but also function of inner horizon at nonasymptotically flat space–time, when a black hole has both inner and outer horizons. Further, the entropy expressed by location parameter of outer and inner horizons approaches zero, when the radiation temperature of a black hole approaches zero. It satisfies the Nernst theorem and can be taken as Planck absolute entropy of a black hole.