Gravitational Field Of A Plasma On The Shadow Of Black Holes

With the advent of the first black hole photo,the theoretical research about black hole shadow becomes very important.Under the theoretical framework of general relativity,for Schwarzschild black hole,Synge first calculates the angular radius of the shadow,and then Bardeen is the first to theoretically analyze the related characteristics of the rotating black hole shadow.However,all these studies are based on a simple assumption that light propagates along the null geodesic and does not interact with matter.Perlick et al.took this work one step forward.Considering the refraction effect of the plasma,the shadow radius and the photon ring radius of the non-rotating black hole were calculated analytically without considering the internal pressure of the plasma.Although the interaction between the photon and the matter was considered,the influence of the plasma mass on the time-space metric was not considered.Based on the research of Perlick et al.,considering a Schwarzschild black hole surrounded by a fully ionized hydrogen plasma,we study the refractive effect and the pure gravitational effect of the plasma on the shadow.The effects are treated in a unified formalism but characterized by two different parameters.For semi-realistic values of parameters,we find their corrections to the shadow radius are both negligible,and the gravitational correction can overtake the refractive correction for active galactic nuclei of masses larger than10⁹ M_?.Since the refractive effect is induced by the electromagnetic interaction,this result is in sharp contrast to the textbook knowledge that the ratio of the gravitational force to the electromagnetic force is Gm_e m_p/e=²4.4×10^-40in a hydrogen atom.With unrealistically large values of parameters,we illustrate the two effects on the light trajectories and the intensity map.The exterior solution of a spherical symmetric black hole surrounded by plasma is studied in detail.After deriving the fundamental equations,the analytic solutions under two kinds of approximate conditions,and are investigated.Comparing the two results with the accurate numerical solution,we find that the latter approximation is better in accuracy,which proves the rationality of the model.