Revision of the brick wall method for calculating the black hole thermodynamic quantities

Within the framework of the "brick wall model", a novel method is developed to compute the contributions of a scalar field to the thermodynamic quantities of black holes. The relations between (transverse) momenta and frequencies in Rindler space are determined numerically with high accuracy and analytically with an accuracy of better than 10 % and are compared with the corresponding quantities in Minkowski space. In conflict with earlier results, the thermodynamic properties of black holes turn out to be those of a low temperature system. The resulting discrepancy for partition function and entropy by two orders of magnitude is analyzed in detail. In the final part we carry out the analogous studies for scalar fields in de Sitter space and thereby confirm that our method applies also to the important case of spherically symmetric spaces.

F. Lenz, K. Ohta, K. Yazaki · 2014