THE BOUSSO ENTROPY BOUND FOR AN IDEAL GAS OF MASSIVE PARTICLES

The Bousso entropy bound is investigated for static, spherically symmetric configurations of an ideal gas with a Bose–Einstein or Fermi–Dirac distribution function. Gas of massive particles is considered. This paper is continuation of the previous work concerning the massless case. Special attention is devoted to light sheets 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 gs 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 gs which is not too large. The situation for higher-dimensional space–times is also discussed and the conditions of Flanagan, Marolf and Wald are investigated.