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We study how a strong gravity affects the equation of state of matters. Forthis purpose, we employ a canonical ensemble of classical monoatomic ideal gasinside a box in a Rindler spacetime. The total energy decreases monotonicallywith the increase of the external gravity representing its attractiveness. Itis however bounded below, which is different from that of the Newtonian gravitycase. As for the entropy, it decreases with the external gravity in theNewtonian regime. However, in the presence of strong gravity orultra-relativistic high temperature, the entropy increases with the gravity.This result can be a resolution of the negative entropy problem of the idealgas in the Newtonian gravity. In the presence of strong gravity, the bottom ofthe box is very close to the event horizon of the Rindler spacetime mimicking ablackhole and the gas behaves as if it is on an effective two dimensionalsurface located at the bottom of the box. Investigating the equation of statein the strong gravity regime, the temperature of the system is found to be nota free parameter but to approach a fixed value proportional to the externalgravity, which is reminiscent of the Unruh temperature.

Matter Equation of State in General Relativity