Study On The Properties Of Black Holes In Einstein-Weyl Gravity

In the context of higher-order derivative gravitational theory,people regard general relativity as a low-energy effective theory,and then try to pass higher-order corrections,hoping that as the energy scale increases,general relativity can be renormalized.In string theory,the Einstein-lilbert action quantity is an initial term,followed by a series of curvature tensor terms and related derivative terms.In string theory,the Einstein—Hilbert action becomes just the first term in an infinite series of gravitational corrections built from powers of the curvature tensor and its derivatives.In other approaches,the possibility is envisaged that just a finite number of additional terms might be added.F or example,if one adds all possible quadratic curvature invariants to the usual Einstein-Hilbert action one obtains a renormalisable theory,namely the Einstein-Weyl gravity,albeit at the price of introducing ghost-like modes in the theory.The main content of the paper:the first chapter introduces the history of relativity theory.As an interesting object-black hole,we briefly introduces the two main aspects of black hole research:black hole thermodynamics and black hole quasinormal modes.Chapter 2 introduces the Einstein-Weyl gravity and two different black hole solutions-S chwarzschild(SBH)and non-schwarzschild(NSBH)black holes.The third chapter uses a new numerical method to derive the charged numerical black hole solutions in the Einstein-Weyl gravity.Here these numerical solutions can be divided into two groups:Group ? and G roup ?:Group ? is a series of charged black hole solutions based on SBH increasing charge Q,and Group ? is charged black hole solutions based on NSBH black hole increasing charge Q.Then,we find the black hole thermodynamic quantity-the mass of the black hole,in order to further study its corresponding thermodynamics and verify the first law of thermodynamics.In Chapter 4,we calculates the quasinormal modes of these black holes under the disturbance of massive and massless scalar field separately,and discuss the stability of black holes in various situations.In Chapter 5,we study the charged AdS black hole solutions surrounded by dust field,radiation field,ACDM field,etc.in the Rastall theory.Later,the black hole phase transition such as reentry phase transition,Vander Waals like large/small black hole phase transition are recovered.