Motion of charged and spinning particle influenced by dark matter field surrounding a charged dyonic black hole

Abstract

We investigate the motion of massive charged and spinning test particles around a charged dyonic black hole spacetime surrounded by perfect fluid scalar dark matter field. We obtain the equations of motion and find the expressions for the four-velocity for the case of a charged particle, and four-momentum components for the case of a spinning particle. The trajectories for various values of electric $Q_e$ and magnetic $Q_m$ charges are investigated under the influence of dark matter field $\lambda$. We find the equations of motion of a spinning particle that follows a non-geodesic trajectory via Lagrangian approach in addition to the charged and non-spinning particles that follow geodesic motion in this set-up. We study in detail the properties of innermost stable circular orbits (ISCOs) in the equatorial plane. The study of ISCOs of a spinning massive particle is done by using the pole-dipole approximation. We show that, in addition to the particle's spin, the dark matter field parameter $\lambda$ and black hole charges ($Q_m\text{and}{Q}_e$) have a significant influence on the ISCOs of spinning particles. It is observed that if the spin is parallel to the total angular momentum $J$ (i.e. $\mathcal{S}>0$), the ISCO parameters (i.e.$r_{ISCO},L_{ISCO}\text{and}{E}_{ISCO}$) of a spinning particle are smaller than those of a non-spinning particle, whereas if the spin is anti-parallel to total angular momentum $J$ (i.e. $\mathcal{S}<0$), the value of the ISCO parameters is greater than that of the non-spinning particle. We also show that for the corresponding values of spin parameter S, the behaviour of Keplerian angular frequency of ISCO ${\Omega }_{ISCO}$ is opposite to that of $r_{ISCO},L_{ISCO}\text{and}{E}_{ISCO}$.

24 pages, 12 captioned figures, 2 tables and 2 appendices, (A new figure added, text modified, to match with the published version in PRD)

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