The Lagrangian of charged test particle in Horava-Lifshitz black hole and deformed phase space

Abstract

We use deformation approach and obtain Lagrangian of charged test particle. We show the effect of non-commutative parameters [Formula: see text] and [Formula: see text] on the Lagrangian of a test particle in Horava-Lifshitz background with charge and without charge and see in the case of [Formula: see text] and without charge, the deformed and non-deformed Lagrangian will be the same. In the case of [Formula: see text] and with charge will be the same but the charge or field need some scaling. Finally, results in the case of [Formula: see text] with charge are completely different. It means that we have other components in addition to having a time component of the field.