| Einstein's general theory of relativity is a geometric theory of time,space and gravity that describes the gravitational interactions between matter.The source of gravity was mass,he thought,and if there was any mass,it would cause space-time to bend.Conversely,it is conceivable that curved space-time also affects the motion of mass.In general relativity,gravity is described as a geometric property of space-time(curvature),and the curvature of space-time is linked by Einstein's field equations to the matter within it and to the energy and momentum of radiation.Einstein's field equations,which describe how matter bends space-time,and the equation of motion of matter,which describes how matter moves in curved space-time,are two fundamental equations that play a very important role in general relativity.General relativity is the most mature theory of gravity at present.In the process of astrophysical research,its theoretical results are consistent with the actual observation.In September 2015,the Laser Interferometer Gravitational-Wave Observatory(LIGO)in the US successfully directly detected gravitational waves generated by binary star mergers,which opened a new era of multi-messenger detection.In addition,humans use the Event Horizon Telescope to take "pictures" of black holes.In 2019,the Event Horizon Telescope(EHT)captured the shadow of the black hole at the center of the elliptical galaxy Messier 87,providing the first visual image of the black hole.The breakthrough directly confirmed the existence of special celestial black holes predicted by general relativity.Set off an upsurge of scholars studying the shadow of black holes.The appearance of the first black hole"photo" makes the study of black hole shadow more and more extensive at home and abroad.Considering that the shadow of a black hole is related to the propagation of light in space-time,if the space-time structure around the black hole changes,it will have some effect on the shadow of the black hole due to gravitational lensing effect.These effects will also reveal more information about black holes,accumulating theoretical results for astronomical observations.The significance of studying black hole shadow is as follows:the image of black hole shadow can be the direct evidence of the existence of black hole;In addition,by observing black hole shadows,it is possible to explore the geometric characteristics of the information carried by dense objects,which means that black hole shadows are a valuable tool for exploring the nature of dense objects and their related gravitational theories.In the past few decades,other theories of gravity have been extensively studied to explain questions that cannot be answered within the framework of general relativity.The hairless theorem states that isolated black holes in Einstein Maxwell's theory are characterized by their mass,charge and angular momentum and cannot produce other non-trivial fields of matter.Since Wheeler came up with this idea,physicists have generalized it to other theories of gravity,such as Brans-Dicke theory,scalar tensor theory,etc.However,physicists have also found some counterexamples.For example,a black hole with Yang-Mills-Higgs hair.In addition,the study of photon zero geodesic around black hole is an important topic,which helps us to understand the properties of black hole and the geometry of space-time.This paper studies the shadow of black hole under the gravity of nonlinear electromagnetic field F(R).It tells that in nonlinear electromagnetic field,the photon will move along the zero geodesic of effective background geometry.The trajectory equation of photon is obtained by using the reverse ray tracing method.The equivalent form of the space-time metric is obtained by referring to the method of M.Novello et al to deal with the photon propagation path in nonlinear electrodynamics.Finally,the dependence of black hole shadow on each parameter is given,and the black hole shadow images with different parameters are analyzed and compared. |
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