Study Of Black Hole Shadow In Modified Gravity

Black holes are one of the predictions of General Relativity(GR).Since the be-ginning of the 20th century,people began to study black holes theoretically,and made many important achievements.In recent years,direct evidences of the existence of black holes have been found through gravitational wave detection and radio astronomi-cal observation.On the one hand,the null geodesics in the strong gravitational region of black hole will form the black hole shadow,and its boundary depends on the trajectory of the photons orbiting it,which in turn is determined by the geometry of spacetime.Therefore,the study of black hole shadow provides an effective way to determine the properties of black holes at the center of galaxies.On the other hand,as the most successful gravity theory,GR still has some unsolvable problems,so some modified gravity theories have been developed.Studying these self-consistent theories will help us understanding GR more deeply.In addition,black holes are often surrounded by accretion due to the strong gravity.Studying the influence of accretion on black hole shadow can correspond to real astrophysical black holes.Therefore,in this thesis,we will investigate the properties of black hole shadow with and without accretion in the background of modified gravity theories.In the first chapter,we will first review the development history of black hole,then briefly introduce the strong gravitational effects of black hole by taking gravitational lens and time bending as examples,and finally give the research motivation and main content of this thesis.In the second chapter,we will introduce the basis of this thesis.Through the mo-tion of light near the black hole,the formation of black hole shadow will be briefly described.Using the Hamilton-Jacobi method,we will take Kerr spacetime as an ex-ample to introduce the motion of photons,including the four equations of motion after separating variables and the radial equation of motion which satisfies the circular orbit conditions.After introducing the celestial coordinates,we will introduce the obser-vational characteristics of Schwarzschild black hole and Kerr black hole shadows in different parameter spaces.Through this chapter,we will have a preliminary under-standing of black hole shadow.In the third chapter,based on our work,we will investigate the appearance and some astronomical observables of rotating and non-rotating black hole shadows in the Modified Gravity(MOG)Theory,and distinguish this theory from GR through shad-ows.In this chapter,we will first review the basic idea of MOG theory and Kerr-like black hole solution.Next,the equations of photon motion are given in this background,and the circular orbit around the black hole is selected from them.On this basis,we will study the properties of the MOG black hole shadow,including the apparent shape and four astronomical observables.Finally,we will study the relationship between the en-ergy emission rate and frequency.The results will show that with the deviation of MOG from GR,the size of black hole shadow will gradually increase and the deformation will decrease.In the fourth chapter,based on our work,we will study the black hole shadow and light deflection angle in the background of Einstein-bumblebee theory,and con-sider the influence of plasma on them.In this chapter,we will study the astronomical observables of black hole shadow in this theory,and then calculate the light deflection angle by Gauss-Bonnet theorem.In the presence of plasma,we will study the influ-ences on shadow and light deflection.Finally,combined with the observational data of M87~*,we will constrain the parameter spaces of the theory and the frequency of plasma.According to the results,we will find a very interesting new phenomenon in Einstein-bumblebee theory.When the observer moves from the two poles to the equator,the shadow radius first decreases and then increases with the Lorentz-violating parameter.Such non-monotonic behavior provides us an important understanding on black hole shadow in Einstein-bumblebee gravity.In the fifth chapter,based on our work,we will investigate the optical appearance of black hole surrounded by thin accretion disks in Einstein-(?)ther theory.There are two forms of spherically symmetric black hole solutions in this theory.First,we will study the motion of photon by Euler-Lagrange method and calculate the total orbital number of photons.According to this,it can be divided into three types:direct image,lensing ring and photon ring,and the trajectory of photons is delineated.Next,combining three toy-models and the relationship between the emission specific intensity and the observed specific intensity of disk,we will describe the optical appearance of the black hole surrounded by thin disk.The results will show that the two coupling parameters in this theory will have different effects on the image.In the last chapter,we will give a summary and an expectation to our future works.Through the above works,we will find that different modified gravity theories will have different effects on the properties of black hole shadow,which provides a new idea for us to distinguish GR from modified gravity.