Bousso entropy bound for ideal gas of massive particles

The Bousso entropy bound is investigated for static spherically symmetric configurations of ideal gas with Bose-Einstein and Fermi-Dirac distribution function. Gas of massive particles is considered. The paper is continuation of the previous work concerning the massless case. Special attention is devoted to lightsheets generated by spheres. Conditions under which the Bousso bound can be violated are discussed and it is shown that a possible violating region cannot be arbitrarily large and that it is contained inside a sphere of unit Planck radius if the number of independent spin states $g_s$ is small enough. It is also shown that the central temperature must exceed the Planck temperature in order to get a violation of the Bousso bound for $g_s$ not too large. The situation for higher-dimensional spacetimes is also discussed and the FMW conditions are investigated.