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

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.

v2, 19pp; added discussions and clarifications, improved presentation; results unchanged; to appear in PRD

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• Decoding infrared imprints of quantum origins of black holes
• A shell of Bosons in Spherically Symmetric spacetimes
• Quantum statistical mechanics near a black hole horizon
• On causality violation on a Kerr-de Sitter spacetime
• A note on entropy of matter in presence of gravity: status of extensivity of entropy
• Microcanonical Phase Space and Entropy in Curved Spacetime