# Entropy of a box of gas in an external gravitational field $-$ revisited

## TL;DR

This paper extends previous work on the entropy of an ideal gas in gravitational fields, showing that entropy exhibits an area dependence near horizons in more general stationary and evolving cosmological spacetimes, including non-static cases.

## Contribution

It generalizes the area dependence of gas entropy to stationary axisymmetric and time-dependent cosmological spacetimes, beyond static cases.

## Key findings

- Entropy develops area dependence near horizons in extended spacetimes.
- Exact results for stationary axisymmetric spacetimes.
- Analytical expression for entropy in near-de Sitter cosmological spacetimes.

## Abstract

Earlier it was shown that the entropy of an ideal gas, contained in a box and moving in a gravitational field, develops an area dependence when it approaches the horizon of a static, spherically symmetric spacetime. Here we extend the above result in two directions; viz., to (a) the stationary axisymmteric spacetimes and (b) time dependent cosmological spacetimes evolving asymptotically to the de Sitter or the Schwarzschild de Sitter spacetimes. While our calculations are exact for the stationary axisymmetric spacetimes, for the cosmological case we present an analytical expression of the entropy when the spacetime is close to the de Sitter or the Schwarzschild de Sitter spacetime. Unlike the static spacetimes, there is no hypersurface orthogonal timelike Killing vector field in these cases. Nevertheless, the results hold and the entropy develops an area dependence in the appropriate limit.