Bardeen Black Hole Surrounded By Perfect Fluid Dark Matter

The singularity theorems states that under the main assumptions of the strong en-ergy condition holds and the global hyperbolicity exists,in the frame-work of general relativity,every black hole inevitably contains a singularity.At the space-time sin-gularity,the curvatures and matter densities go to infinity,and the predictive power of physical laws is completely broken down.However,it is widely believed that the space-time singularities are the reflection of the incompleteness of General Relativity,which can be solved in a quantum theory of gravity.Although there are no mature and reliable candidates for quantum gravity theory,some toy models without singularity black hole solutions have been proposed.As one of the most famous models,Bardeen black hole is interpreted as a gravitationally collapsed magnetic monopole arising in a specific form of nonlinear electrodynamics.According to astronomical observation,black holes in reality are always in dark matter,so we focus on the case that they are surrounded by the perfect fluid dark matter in this thesis.In the chapter I,we first introduce the research background,content and organi-zational structure of the paper.Then,we review the basic knowledge of black holes,including the properties of Kerr black holes,black hole thermodynamics and electrody-namics.Taking the common Kerr black hole as an example,we give the proof of the black hole thermodynamics law and the Smarr formula in detail,and show the calcula-tion of the related basic thermodynamic quantities.Finally,we introduce the nonlinear electrodynamics of black holes in curved spacetime.In the chapter II,we derive the exact solution of Bardeen black hole surrounded by perfect fluid dark matter.By treating the parameter of dark matter as a new thermo-dynamic variable,we find that the first law of thermodynamics and the corresponding smarr formula are still valid.Furthermore,we study the thermodynamic stability of black holes.The result show that,there exists a critical radius r_+~C,where the heat ca-pacity diverges,suggesting that the black hole is thermodynamically stable in the range0<r_+<r_+~C.In addition,the critical radius r_+~Cincreases with the magnetic charge g and decreases with the dark matter parameter?.Further,by studying the quasinor-mal modes of scalar perturbations in the space-time of black holes,we also discuss the dynamic stability of Bardeen black holes in the perfect fluid dark matter.In the chapter III,applying the Newman-Janis algorithm,we extend the above spherical symmetric solution to the corresponding rotating black hole solution.Next,we examine the weak energy condition.By means of the obtained metric,we also study the horizons and ergospheres.It turns out that for a fixed dark matter parameter?,in a certain range,with the increase of the rotation parameter a and magnetic charge g,the Cauchy horizon radius increases while the event horizon radius decreases.At the end of this chapter,we also investigate the energy extraction by the Penrose process in rotating Bardeen black hole surrounded by perfect fluid dark matter.Finally,we summarize the study of this thesis,and look forward to the prospects of the future work.