American Astronomical Society, Astrophysical Journal, 2(726), p. 80, 2010
DOI: 10.1088/0004-637x/726/2/80
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Recently, some intriguing results have led 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 β0 ≤ 1/2. Furthermore, we present several systems with β0>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 toward an understanding of the relation for general spherical systems.