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Entropy of a box of gas in an external gravitational field $-$ revisited
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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.
Forward citations
Cited by 2 Pith papers
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A note on entropy of matter in presence of gravity: status of extensivity of entropy
In a strong uniform Newtonian gravitational field, the entropy of a monoatomic ideal gas depends on the container's cross-sectional area and is extensive when particle number per unit area is fixed.
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