Geodesics And Black Hole Shadows Of The Bardeen-de Sitter Black Hole

As the most successful theory of gravity at present,general relativity is not only because it can successfully describe the physics in the scope of the solar system,but also because of the improvement of people's observation level,its correctness is more and more confirmed.However,the problems posed by general relativity are also puzzling,and black hole singularities are one of them.Space-time curvature and matter density tend to infinity at singularity,so existing rules of physics no longer apply.To solve the singularity problem,attention has turned to quantum gravity.Although there is no fully convincing quantum gravity theory yet,this does not prevent scientists from proposing a black hole solution model without singularity,such as the Bardeen black hole formed by gravitational collapse under nonlinear electromagnetic fields.Furthermore,according to astronomical observations,our universe is now in a state of accelerated expansion.To explain the phenomenon of accelerated expansion,scientists introduced a cosmological constant term in Einstein's field equations that provided the repulsive force and interpreted it as "dark energy".Therefore,this paper will study the geodesics and black hole shadows of Bardeen black hole under the influence of the cosmological constant.First,we will introduce the corresponding research background,content and structural framework of the paper,and make some brief reviews of related knowledge.Then,we calculated the time-like and null geodesic equations of the Bardeen-de Sitter black hole through the Hamiltonian equation.And through the effective potential of the particle,the different types of orbits that the geodesics may exist under different parameter values are discussed.After calculation,it is found that the introduction of the cosmological constant term will make the time-like geodesics different from the asymptotically flat space-time,and new unstable orbits will appear at positions far from the black hole,but has no effect for null geodesics.Finally,by rotating the Bardeen-de Sitter black hole solution,the black hole structure and the effects of different parameter changes on the black hole structure are discussed,such as the horizon and photon region.For black hole shadows,we will discuss black hole shadows corresponding to different observers.For standard observers and zero angular momentum observers,we will use the method of constructing the observer's orthonormal tetrad to calculate the shadow of the black hole.For static observers,we will determine the outline of the black hole's shadow using a method for calculating the angle between the tangents of the space-time null geodesic.We also discuss the effect of different parameters on the shadow profile,and finally compare the differences in black hole shadows observed by different observers.It was found that the closer the distance to the black hole,the greater the shadow deformation corresponding to the zero angular momentum observer,while the farther away from the black hole,the results of the three observers are consistent.