Effects of Quantum Gravity on Thermodynamic Quantities of Gases around a Novel Neutral Four-Dimensional Gauss–Bonnet Black Hole

Abstract

Taking the generalized uncertainty principle (GUP) into account, we apply the corrected state density to investigate the entropy density, energy density, pressure and equation of state for the perfect relativistic gases of massless particles with an arbitrary spin of s ≤ 2 surrounding a new four-dimensional neutral Gauss–Bonnet black hole. The modifications of these thermodynamic quantities by the gravity correction factor and particle spin are shown, and the expressions have completely different forms from those in flat space-times. For example, the energy density is not proportional to the fourth power of the temperature. In other words, the energy density differs from that of blackbody radiation. The quantum gravity effects reduce these quantities and are proportional to the gravity correction factor. The result that the equation of state is not zero is compatible with the non-vanishing trace of the stress tensor.