Matter Equation of State in General Relativity

TL;DR

This paper explores how strong gravitational fields influence the thermodynamic properties of an ideal gas in Rindler spacetime, revealing novel behaviors of energy and entropy under extreme gravity conditions.

Contribution

It introduces a model of an ideal gas in strong gravity, showing how gravity affects energy, entropy, and temperature, and suggests a link to black hole physics and the Unruh effect.

Findings

Energy decreases monotonically with gravity, bounded below.

Entropy increases with gravity in strong or ultra-relativistic regimes.

Temperature approaches a fixed value proportional to gravity, similar to Unruh temperature.

Abstract

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.