Elastic monopoles and external torques in nematic liquid crystal colloids

Up to now it is commonly believed that a colloidal particle suspended in a nematic liquid crystal never produces elastic monopoles because this violates the mechanical equilibrium condition. And the only way to obtain deformations of director field falling off with distance as r^{-1} is to exert an external torque \Gamma_{ext} on the colloid \cite{de_Gennes}. In this paper we demonstrate that this statement is not quite correct and elastic monopoles, as well as dipoles and quadrupoles, can be induced without any external influence just by the particle itself. A behavior of a spherical colloidal particle with asymmetric anchoring strength distribution is considered theoretically. It is demonstrated that such a particle when suspended in a nematic host can produce director deformations decreasing as $r^{-1}$, i.e. elastic monopoles, by itself without any external influence.