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

TL;DR

This paper derives the Lagrangian for a charged test particle in a Horava-Lifshitz black hole background using deformation methods, analyzing the effects of non-commutative parameters and revealing differences based on parameter choices.

Contribution

It introduces a deformation approach to obtain the Lagrangian of charged particles in HL black holes and explores the impact of NC parameters on the dynamics.

Findings

Deformed and non-deformed Lagrangians coincide when = without charge.

For = with charge, Lagrangians are similar but require scaling.

Different theories emerge when d7, indicating distinct NC geometries.

Abstract

In this paper, we use deformation approach and obtain the corresponding Lagrangian of charged test particle. Also, we show the effect of NC parameters on the Lagrangian of test particle in HL background with charge and without charge. Also, we see in case of $\beta=\theta$ and without charge, the deformed and non-deformed Lagrangian will be same. Also in case of $\beta=\theta$ and with charge will be the same but the charge or field need some scaling. Finally, We show that two theories in case of $\beta\neq\theta$ with charge is completely different. It means that in case of NC geometry in addition to have time components of field we have $r$ and $x_{i}$ components.