Thermodynamic quantities for gases in static spherically symmetric backgrounds possessing a horizon

We use the brick-wall method to study the thermodynamic quantities for the perfect relativistic gases in a generic spherically symmetric and static background spacetimes possessing a horizon. We employ the Wentzel-Kramers-Brillouin (WKB) approximation on the Teukolsky-type master equation. We show that the entropy density, energy density, pressure and state equation all contain a subleading term, which depends on the spins of the particles of gases. When particularizing to Schwarzschild and Reissner-Nördstrom geometries we recover the results previously found in the literature for those geometries.