Chaos Of Particle Motion In Rotating Black Hole Spacetime

Chaos is a kind of disorder motion occurred in the nonlinear dynamic system under certain conditions.Since that the dynamic equations of gravity and cosmology in general relativity are often highly nonlinear equations of motion,the study of chaos can help us to understand deeply the wonderful universe.In this thesis,we use the Lyapunov indicator,Poincare section,bifurcation and fractal methods to study the chaotic phenomenon of particles in rotating black hole spacetime in two kinds of gravity theory.First,we give a brief introduction to chaos and its main research methods.Second,we study the chaos of scalar particle motion coupled with Chern-Simons invariants in Kerr black hole spacetime.Our results show that the coupled dynamic system are not integrable.With the increase of the coupling strength,the motion of the coupling particles for the selected parameters first experiences a series of transitions between chaotic motion and regular motion,and then falls into the horizon or escapes to the infinite space.In addition,we also discuss the influence of black hole spin parameters on the motion of coupled scalar particles.Finally,we find that the existence of coupling makes the motion of particles in rotating Kerr black hole have self similar fractal structure.Therefore,the coupling of scalar particles with Chern Simons invariants greatly enriches the dynamic behavior of scalar particles.Third,we study the chaotic phenomena of particle motion in the disformal rotating Kerr black hole spacetime in DHOST theory.It is shown that chaos occurs in the particle's dynamics system for the rapidly rotating black hole.By analyzing the Poincare section,for the positive deformation parameter,we find that the orbits of particle motion are all stable and their radius increase with the increase of the deformation parameter.For the negative deformation parameter,the motion of particles is limited in the very near region of the black hole.With the increase of the deformation parameter(absolute value),the main stable island in Poincare section tends to shrink,and the chaotic region first increases and then disappears because the particles fall into the black hole after a short time motion.Finally,we presented a summary and make some prospects of the chaotic phenomena in black hole spacetimes.