Spin-Dependent Term of Thermodynamic Quantity Around a Black Hole

The entropy density, energy density, pressure, and equation of state of an ideal relativistic gas around the Schwarzschild-anti-de Sitter black hole with a global monopole are investigated by using the brick-wall method. It is shown that the sub-leading term with spin-dependence exists and that the corrected expression for any spin field is very different from that for scalar field. The usual result that these thermodynamical quantities take the same forms as those in flat spacetime holds only for the leading term.