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.
