  A new analysis of elastic properties of dense hard sphere (HS) fluids is
presented, based on the expressions derived by Miller [J. Chem. Phys. {\bf 50},
2733 (1969)]. Important consequences for HS fluids in terms of sound waves
propagation, Poisson's ratio, Stokes-Einstein relation, and generalized Cauchy
identity are explored. Conventional expressions for high-frequency elastic
moduli for simple systems with continuous and differentiable interatomic
interaction potentials are known to diverge when approaching the HS repulsive
limit. The origin of this divergence is identified here. It is demonstrated
that these conventional expressions are only applicable for sufficiently soft
interactions and should not be applied to HS systems. The reported results can
be of interest in the context of statistical physics, physics of fluids, soft
condensed matter, and granular materials.
