Optical Properties Of Hayward Black Hole Surrounded By Perfect Fluid Dark Matter

The singularity of black hole reveals the incompleteness of general relativity.This problem may be solved in a theory of quantum gravity,but scientists have not yet found an ideal theory of quantum gravity.Hayward black hole is thought to be a nonlinear magnetic charge collapsing black hole whose center avoids a singularity in the form of de Sitter geometry.As a toy model,it has been extensively studied in recent years.On the other hand,the Standard Model of the Universe says that the proportion of dark matter in the universe is no less than 1/4.This paper mainly studies the optical properties of Hayward black hole in perfect fluid dark matter(PFDM).In the chapter I,we introduce the research background and content of this thesis,and review the basic knowledge of general relativity.In the chapter II,we derive the spherical symmetric solution of the Hayward black hole surrounded by PFDM,and then study the effects of the magnetic charge parameter Q and the PFDM parameter k(k<0)on the light trajectory.Further,we consider the imaging of three thin accretion disk models,and the calculation results show that the observed intensity of the accretion disk mainly comes from the contributions of"direct light"and"lensing light".PFDM makes the image of the accretion disk larger and darker,and the magnetic charge has little effect on the image.The images produced by different accretion disk models vary widely.Our calculation results may provide a reference for the observation of PFDM and the experimental discrimination of accretion disk types.In the chapter III,with the help of the Newman-Janis(NJA)method,we generalize the spherical symmetry solution to the rotating black hole solution.Then,we study the shadow of black hole and show that the rotation parameter a deforms the shadow.In addition,we study the effects of the magnetic charge parameter Q and the PFDM parameter k on the black hole shadow radius Rs and the distortion parameter?s,the results show that Rs increases with the increasing|k|,but decreases with the increasing Q.Taking a non-zero value of a,we find that?sincreases with the increase of Q,but the relationship between?sand k is not monotonic,there exists a k0,which minimizes the deformation parameter?s.Finally,taking the supermassive black hole Sgr A^*as an example,we calculated the angular size?sof the black hole,we find that it is easier to extract the information of PFDM parameter k by optical methods,but it is difficult to extract the informaton of black hole spin parameter a and magnetic charge parameter Q.Finally,we summarize the work of this thesis and give an outlook on future re-search.