The Effect Of Dark Matter On The Phase Transition Of Black Holes And The Study Of Mutual Correlation In Phantom Ads Black Hole

Our research mainly consists of two parts.On the one hand,under the framework of generalized uncertainty principle(GUP),based on the quantum tunneling radiation theory,we discussed the influence of dark matter on thermodynamics and phase transition in Schwarzschild-XCDM black hole in the membrane world.On the other hand,based on shock wave geometry and chaos theory,mutual correlation and chaos behavior were studied in the phantom Ads black hole.Through the research,we had obtained many results worthing in-depth analysis and thinking.Firstly,we used GUP to modified the tunneling radiation of scalar and vector particles in Schwarzschild-XCDM black hole under the influence of dark matter.Then,we calculated the modified tunneling rate,Hawking temperature,heat capacity of the GUP and so on.The relationships between the thermodynamic quantities under the influence of dark matter parameters were discussed,such as the local temperature-mass,heat capacity-mass and local free energy-local temperature.It was found that,compared with Schwarzschild black hole and Schwarzschild Ads black hole,GUP can prevent the Schwarzschild-XCDM black hole from completely evaporating in the later stage of black hole evolution,and lead to the generation of black hole remnant.In addition,there was a Hawking page-like phase transition related to dark matter parameters,and its critical temperature decreases with the increase of dark matter.Compared with the spherical symmetric black hole in the GUP framework with only one phase transition,it turned out that dark matter can greatly change the phase diagram of the black hole from these new plots.Under different parameters of dark matter,the first-order phase transition,the second-order phase transition and the Hawking page-like phase transition can be observed.In addition,by analyzing the mutual correlation of the shock wave geometry in the static background,we can find that the mutual correlation increased with the increase of the black hole charge,and the boundary separation had a similar relationship with the the dark energy parameter.Then,the mutual correlation and chaotic behavior of phantoms Ads black hole under dynamic background were further studied by adding light-like energy disturbance to the system.The results showed that the larger the energy disturbance is,the faster the mutual correlation is destroyed,which is similar to the butterfly effect in chaos theory.