  We study how a strong gravity affects the equation of state of matters. For
this purpose, we employ a canonical ensemble of classical monoatomic ideal gas
inside a box in a Rindler spacetime. The total energy decreases monotonically
with the increase of the external gravity representing its attractiveness. It
is however bounded below, which is different from that of the Newtonian gravity
case. As for the entropy, it decreases with the external gravity in the
Newtonian regime. However, in the presence of strong gravity or
ultra-relativistic high temperature, the entropy increases with the gravity.
This result can be a resolution of the negative entropy problem of the ideal
gas in the Newtonian gravity. In the presence of strong gravity, the bottom of
the box is very close to the event horizon of the Rindler spacetime mimicking a
blackhole and the gas behaves as if it is on an effective two dimensional
surface located at the bottom of the box. Investigating the equation of state
in the strong gravity regime, the temperature of the system is found to be not
a free parameter but to approach a fixed value proportional to the external
gravity, which is reminiscent of the Unruh temperature.

General Relativity and Quantum Cosmology;High Energy Astrophysical Phenomena;High Energy Physics - Theory