On the universality of the global slope -- anisotropy inequality
  Recently, some intriguing results have lead to speculations whether the
central density slope -- velocity dispersion anisotropy inequality (An & Evans)
actually holds at all radii for spherical dynamical systems. We extend these
studies by providing a complete analysis of the global slope -- anisotropy
inequality for all spherical systems in which the augmented density is a
separable function of radius and potential. We prove that these systems indeed
satisfy the global inequality if their central anisotropy is $\beta_0\leq 1/2$.
Furthermore, we present several systems with $\beta_0 > 1/2$ for which the
inequality does not hold, thus demonstrating that the global density slope --
anisotropy inequality is not a universal property. This analysis is a
significant step towards an understanding of the relation for general spherical
systems.
