On the global density slope-anisotropy inequality

Abstract

Starting from the central density slope-anisotropy theorem of An and Evans (2006), recent investigations have shown that the involved density slope-anisotropy inequality holds not only at the center, but at all radii (i.e. globally) in a very large class of spherical systems with positive phase-space distribution function. Here we present some additional analytical cases that further extend the validity of the global density slope-anisotropy inequality. These new results, several numerical evidences, and the absence of known counter-examples, lead us to conjecture that the global density slope-anisotropy inequality could actually be a universal property of spherical systems with positive distribution function.

6 pages, proceedings of the international symposium "Plasmas in the laboratory and in the universe: interactions, patterns, and turbulence", Como 1-4 Dec. 2009, eds. G. Bertin et al., AIP Conf. Ser