Numerical Simulation And Theoretical Analysis For Black Hole Shadow

Event Horizon Telescope is an ongoing important scientific program of detect-ing black holes at present in the world.Its main purpose is to obtain the visual images of the black hole in the galactic center Sgr A*and the black hole in M87 galaxy center.These visual images are very important for people to further verify the existence of black hole,to study and understand physical phenomena including the matter accretion process into black hole and the production of black hole jets.One of the main component in these visual images is shadow of black hole,which carries a lot of important information of the black hole.Therefore,it is very im-portant and necessary to research the shadow of black hole.In this thesis,we have studied the main features of the shadow casted by a rotating Konoplya-Zhidenko black hole and of the black hole shadows caused by chaotic motion of photons in spacetimes.We also probe the formation mechanism about black hole shadows.In the first chapter,we make a brief introduction on the shadows of black holes and their research significance,as well as the formation of black hole shadow.In the second chapter,we studied the shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole with an extra deformation parameter ?.We found that the spacetime structure arising from the deformed parameter affects sharply the black hole shadow.With the increase of the deformation parameter,the size of the shadow of black hole increase and its shape becomes more rounded.D-shape shadow appears only if:(i)a<M and the deformation parameter tends to a critical value ?c1=-2/2(?)+2M)2((?)-M);(ii)M<a?(?)M and the deformation parameter tends to the value ?c1 from positive direction.Moreover,the cusp silhouette with small eye lashes appears in the shadow of a Konoplya-Zhidenko black hole,which is a novel shape for black hole shadows.The condition of existing cusp silhouette is:(i)M<a<(?)M and the deformation parameter ?/<?c1;(ii)a>(?)M and the deformation parameter is below a certain value which depends on the rotation parameter numerically.We also analyzed the fundamental photon orbits in the rotating Konoplya-Zhidenko black hole spacetime,and found that there is a jump occurred in the size of these fundamental photon orbits at some points,which yields that the boundary of black hole shadow is not smooth and then the cusp shadow occurs.In the chapters three to five,we simulate numerically the black hole shad-ow as the chaotic motion occurs for photons propagating in the spacetime by the technique of backward ray tracing.Moreover,we also probe the formation mech-anism by using of the invariant phase-space structures.In the third chapter,we investigated the shadows of Bonnor black dihole.As the magnetic moment pa-rameter b<bc?0.404,the shadow of Bonnor black dihole is a black disk.As b>bc,there are two anchor-like bright zones embedding symmetrically in the black shadow.The anchor-like bright zones become bigger with the increase of b.Moreover,there are some self-similar fractal structures appeared in the black hole shadow.We also analyzed the invariant phase-space structures and the unstable manifold for photon dynamical system in the Bonnor black dihole spacetime and probed how these phase-space structures and unstable manifold play roles in the formation of black hole shadow.In the fourth chapter,we studied the shadows of a non-Kerr rotating compact object with an deviated parameter q related to the quadrupole mass moment.As the quadrupole-deviation parameter q is negative,the shadow of compact object is split into two disconnected shadows,which lie at symmetric positions above and below the equatorial plane.With increase of |q| the shadow becomes more prolate.As q is positive,the shadow is joined together in the equatorial plane and it is more oblate with the parameter q.In the case with the positive q,.there is a disorder region in the left of shadow which increases with the increase of q.As in other photon non-integrable dynamical systems,there also exist some self-similar fractal structures in the shadow.Moreover,we found that the Einstein ring is broken for the absolute value of q grater than a certain critical value |qc|.The critical value |qc| decreases with the rotation parameter S of Manko-Novikov compact object.Finally,we assumed the supermassive black hole in the Milk Way can be described by a rotating Manko-Novikov compact object,and then investigated the dependence of some observables on the spacetime parameters.In the fifth chapter,we investigated the shadows of Schwarzschild black hole with Bach-Weyl ring.As Weyl radius b between black hole and Bach-Weyl ring is large,the presence of Bach-Weyl ring leads to that the shadow becomes thin in the middle and rough at the ends so that it has "8" shape.As the ring becomes close to the black hole,i.e.,b decreases,the shape of shadow become a circle gradually and its size increases.As the parameter is in a certain a range,there are some fractal structures appeared in the shadow.Therefore,the emergence of fractal structures is a common feature of the black hole shadow as the chaotic motion occurs in the photon propagations.Furthermore,we have also studied the important role of the invariant space structure and unstable manifold in the formation of black hole shadow.Finally,we presented a summary and make some prospects for the investigation of black hole shadows.