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

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 β = θ and without charge, the deformed and non-deformed Lagrangian will be same. Also in case of β = θ and with charge will be the same but the charge or field need some scaling. Finally, We show that two theories in case of β = θ 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.

The equivalence between Finsler and non-commutative geometries by massive gravity black hole

“…Another QG approach is associated with the application of NC geometry for CQG with the deformed space-time as the main attitude in the present paper. This kind of non-commutativity is applied to our recent cosmological papers [7][8][9]. On the other hand, we want to present some explanations about Finsler as a second target geometry.…”