Black Hole Shadow And Gravitational Lensing

Einstein's general theory of relativity changed people's understanding of time and space.For more than a hundred years,the predictions of general relativity have been realized time and time again,and have withstood the test of all current experiments.Physicists are increasingly confident in general relativity.At the same time,physicists' exploration of new gravitational theories has not slowed down,and various gravitational theories have appeared one after another.Some observable gravitational effects have become powerful tools to test the theory of gravity.In this article,we mainly discuss two important gravitational effects,namely the shadow of black holes and the weak gravitational lensing of black holes.In the first chapter of this article,we introduced the mathematical basis of the full text,mainly involving hypersurfaces and geodesic curvature.A considerable part of the content of this part of the introduction is the author's own understanding of the corresponding content,especially the part of geodesic curvature.In the black hole shadow part,we introduced the basis of calculating the black hole shadow in detail,and added some content omitted in the literature.Then,we apply this theory to the calculation of the rotating Hayward de Sitter black hole,and combine the image to analyze how the size and shape of the black hole shadow changes with the various parameters of the black hole and the position of the observer.These theoretical analyses can provide references for related experiments.Regarding the gravitational lensing,we first introduced the Gauss-Bonnet(GB)theorem.After that,we introduced the application of GB theorem in calculating static spherically symmetric space-time or stationary axisymmetric space-time.In order to calculate the Gaussian curvature,geodesic curvature and light deflection angle,specific calculation formulas are given,and GB theorem is applied to the gravitational lensing of a rotating four-dimensional Einstein-Gauss-Bonnet(EGB)black hole.Theoretical research on these observable effects may have an impact on experiments to test the theory of gravity.