Modified Hawking Tunneling Radiation Of Black Holes Under Lorentz Invariance Violation And Its Related Problems

In the early twentieth century,the theory of general relativity was pioneered by Albert Einstein,in which the gravitational field could be described by geometric curvature,and since then people's perception of spacetime has changed by leaps and bounds.The general theory of relativity predicted the existence of black holes,the most special object in the universe,and the black hole image has indirectly confirmed the existence of black holes.With the study of black holes by Hawking,Bekenstein and Penrose,it has been found that black holes can be used to communicate general relativity,quantum mechanics and thermodynamics.After taking into account quantum effects,Hawking discovered that a black hole is not completely black,but emits radiation as a black body and has its own entropy.But currently people still have not been able to create a complete theory of quantum gravity.The study of quantum gravity theory is one of the current frontier problems in physics,and there are two main effective models:Lorentz invariance violation and general uncertainty principle.In this thesis,the fermion tunneling radiation of stationary axisymmetric black holes is studied using the modified dispersion relation under Lorentz invariance violation to discuss the change of thermodynamic properties of black holes.In the first introductory chapter of this paper,we give the introduction to gravity,black holes and black hole thermodynamics.Chapter 2 we review the gravitational perturbation master equations in flat spacetime and Schwarzschild spacetime,and summarize how to solve the likelihood scale of black holes by WKB method,Horowitz-Hubeny method and matrix method using Mathematica software.Chapter 3 introduces the modified theory of gravity,reviews the modified Hamilton-Jacobi equation under Lorentz invariance violation,and obtains the kinetic equations describing fermions in curved spacetime.In Chapter 4,we further study the fermion tunneling radiation of black holes and the thermodynamic properties at the event horizon.We discuss the effect of dispersion relations on the thermodynamics of black holes.We found that the Hawking temperature and the entropy of the black hole need certain changes,which will make the radiation of the black hole evaporate faster.Interestingly,compared with the GMGHS black hole,the Demianski-Newman black hole and the Kerr-NUT black hole,the modified Hawking temperature and the black hole entropy of the EMDA black hole are not only related to the correction parameter and particle mass,but also to the angle parameter.