Bardeen Black Hole In Einstein-Gauss-Bonnet Gravity

In general relativity,black holes are the final products formed after the gravitational collapse of massive stars.Physicists have studied them for more than a hundred years,but they have always been theoretical studies and have not been observed experimentally.In the last ten years,with the progress of experimental methods,the gravitational waves of the merger of double black holes were finally detected in 2016 and the first black hole photo was released in 2019.We were finally able to experimentally confirm the existence of black holes.The theoretical study of black holes has been confirmed.In solving the Einstein field equations,the solutions of black holes will have singularities in the case of high symmetry.Many physicists believe that the symmetry of these solutions is too high to be a real physical black hole solution.The singularity is in the real Non-existent in the physical world,singularities are entirely the result of a high degree of symmetry.But in 1965 Penrose did not use any symmetry assumptions to prove that a star collapsed below the Schwarzshilcd radius would have singularities.Later Hawking and Penrose proved a series of singularity theorems for the more general case.But then in 1968 B ardeen obtained a singularity-free black hole solution in the vacuum-like equations for matter.But the physical meaning of this black hole solution was not clear at the time,and it only received attention when Ayon-Beato and Garcia understood it as a magnetic monopole black hole produced by gravitational collapse under a special form of nonlinear electromagnetic field.At the same time,Gauss-Bonnet gravity is an extended gravitational theory that considers the contribution of higher-order curvature terms,and the natural deduction of the low-energy effective amount of string theory has also been widely studied.This paper hopes to study the properties of Bardeen black holes under EinsteinGauss-Bonnet((EGB)gravity.The full text is divided into four chapters.In the first chapter,we briefly review some basic knowledge of black holes,the regularity of Bardeen black holes,black hole thermodynamics and Hawking radiation;in Chapter 2 we introduce EGB gravity,deduce the metric of the Bardeen black hole under EGB gravity,and study its black hole shadow and thermodynamic properties;in Chapter 3,we briefly introduce the background knowledge and calculation of the quasi-normal scale method,and then we consider the quasi-positive scale of the Bardeen black hole under EGB gravity under the scalar field and vector field perturbation,respectively,and also study the relationship between the black hole shadow radius and the quasi-positive scale,and finally,we also give the transmission probability.Chapter 4 We summarize our work and give an outlook.