Orbital Dynamics Of A Non-linear Magnetic Charged Black Hole Surrounded By Quintessence And Clifton—Barrow Black Hole

Cosmological observations?such as supernova type Ia,etc.?show that our universe is currently accelerating its expansion.This conclusion enriches the study of the evolution of the universe.In order to explain the accelerated expansion of the universe,scientists put forward the concept of”dark energy”,which is a kind of energy with strong negative pressure and can produce repulsion.According to relevant research,dark energy is about70%of the total energy density of the universe.We can understand the universe better by studying dark energy.In physics,quantum mechanics and general relativity can not be completely unified,but the intersection of the two theories can be found by understanding dark energy,so the research of dark energy is of great significance.In addition,modified theory of gravity,such as f?R?gravity,can also be used to explain the accelerated expansion of the universe.In this paper,we mainly study the orbital dynamics of the non-linear magnetic charged black hole surrounded by quintessence and Clifton—Barrow black hole.The results show that:?1?In the space-time of a non-linear magnetic charged black hole surrounded by quintessence,by solving Lagrangian equation 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.The influence of quintessence on orbit type and stability is discussed.In addition,for time-like orbital motion,when 3.443113?b?6.392578?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=5.912654 and r=56.745933,respectively.For null orbital motion,the orbital types has only unstable circular orbit which occur at r=2.951072?E²=E₂²=0.4?,absorb orbits and escape orbits,but no stable circular orbits and bound orbits.?2?In the space-time of Clifton?Barrow black hole,through the numerical analysis of the effective potential and the motion equation,the orbital types of test particles and photons and the corresponding orbital motion diagrams of each orbital types under certain conditions are obtained.We find that angular momentum b and?determine the existence of bound orbits and circular orbits.And we also find that the radius of unstable circular orbit decreases with increases in b while the radius of stable circular orbit increases.Furthermore,as?increases,the radius of unstable circular orbit increases,while the radius of stable circular orbit decreases.For null geodesic,parameters b and?do not affect the types of null orbits.The radius of the unstable circular orbit increases with the increase of?.However,with the increase of the angular momentum of b,the radius of the unstable circular orbit will keep a constant value.Also,we prove that the bound orbit of the test particle has a precession direction,and the precession direction is determined by the angular momentum of b.For example,when angular momentum b=2.15,the precession direction is counterclockwise,while when angular momentum b=3.6,the precession direction is clockwise.Moreover,different energy values have an effect on the curvature of escape orbits and absorb orbits curve.