Geodesic Structure of a Non-linear Magnetic Charged Black Hole Surrounded by Quintessence**Supported partly by the National Natural Science Foundation of China under Grant No. 11565016, the Special Training Program for Distinguished Young Teachers of the Higher Education Institutions of Yunnan Province under Grant No. 1096837802, and the Applied Basic Research Programs of Yunnan Provincial Science and Technology Department under Grant

Abstract

This paper aims to investigate the geodesic motion in the spacetime of a non-linear magnetic charged black hole surrounded by quintessence. By varying the Lagrangian corresponding to the metric, the orbital motion equation has been obtained. The effects of the magnetic charge Q, positive normalization factor C, angular momentum b, and energy E on time-like and null geodesic motion are discussed from three aspects: orbital stability, orbital types, and circular orbits. By comparing the effects of the above parameters C, b on the effective potential, it is found that quintessence has an impact on the types and stability of orbits. In addition, for time-like orbital motion, when 3.443113 ≤ b ≤ 6.392 578 (for fixed C = 0.0002, M = 1, Q = 0.7), there are bound orbits, and within this range, the stable circular orbits exist, and the radii of the innermost and outermost stable circular orbit are r = 5.912 654 and r = 56.745 933, respectively. For null orbital motion, the orbital types have only unstable circular orbit which occur at r = 2.951 072 (), absorb orbits and escape orbits, but no stable circular orbits, and bound orbits.