Holographic Mutual Information And Mutual Correlation And Butterfly Effect Of AdS Black Hole

In this paper,the butterfly effects of three different AdS black holes are studied by taking the nonsingular Hayward AdS black hole,the novel Gauss-Bonnet AdS black hole and the Reissner-Nordstr?m AdS black hole with dark energy surrounded by quintessence as examples.Hayward black hole is an analytical solution of Einstein ’s gravitational nonlinear coupling of an electromagnetic field carrying magnetic charges.Hayward black hole is a degenerate structure of the nonlinear magnetic monopole gravitational field.The symmetry of the regular black hole is determined by the magnetic potential,and the magnetic charge and the non-magnetic charge have different microstructures.We discuss the influence of magnetic charge on holographic mutual information in nonsingular Hayward AdS black hole by using entanglement entropy.The results show that the entanglement of the two asymptotic subsystems increases with the increase of the strip width(subregion).After adding light-like energy perturbation to the system,it is found in the shock wave geometry that the larger the magnetic charge,the smaller the critical value of the horizon shift,and the magnetic charge will weaken the correlation between the two subsystems.The larger perturbation will destroy the correlation more quickly,which is completely similar to the butterfly effect in chaos theory.Secondly,we study the influence of the Gauss-Bonnet coupling constant and charge on butterfly effect in the novel Gauss-Bonnet AdS black hole by using mutual correlation.In the static background,it is found that as long as the area considered on the boundary is large enough,the two subregions on the AdS black hole boundary are correlated.The mutual correlation is inversely proportional to the charge and decreases with the increase of the Gauss-Bonnet coupling parameter.Adding a light-like energy disturbance at the AdS boundary will form a dynamic shock wave geometry after a long time.In this dynamic background,it is found that the larger the translation of the horizon,the smaller the mutual correlation.When the translation is large enough,the mutual correlation disappears,and the boundary regions of the two subsystems are not correlated.The mutual correlation in the dynamic background decreases with the increase of charge and is inversely proportional to the Gauss-Bonnet coupling parameter,which is the same as that in the static background.It is found that the neutral novel Gauss-Bonnet AdS black hole has the same butterfly effect as the charged novel Gauss-Bonnet AdS black hole.In addition,this paper also studies the butterfly effect of Reissner-Nordstr?m AdS black hole with dark energy by using the mutual correlation.The results show that the larger the charge,the smaller the mutual correlation value.After adding the energy disturbance,the mutual correlation disappears when the translation is large enough,and the boundary region is irrelevant.It means that black holes with dark energy also have the butterfly effect.