| In this thesis,the perturbations and fluctuations in(1+1)-dimensional point matter black hole and non-commutative black hole are studied.In Chapter 1,the research history of black hole is reviewed,and research status of(1+1)-dimensional gravitation,non-commutative theory and analogical gravity are introduced.In Chapter 2,how to eliminate the difficulty of “IR/UV” divergence in non-commutative field theory is studied,the energy density fluctuations of scalar field in non-commutative universe are calculated,the energy density fluctuation of Fermi matter in two-dimensional non-commutative space-time are also derived.In Chapter 3,the motion properties of classical particles in two-dimensional black holes are studied,and the falling time of mass particles in point matter black hole and non-commutative black hole is calculated respectively by solving the geodesic equation when the gravitational field is perturbed.In Chapter 4,the quantum fluctuation properties of scalar field in two-dimensional black holes are studied,and the energy density fluctuations of scalar field in point matter black holes and non-commutative black holes are derived by using the solution of Klein-Gordon equation when the gravitational field is perturbed.In Chapter 5,the quantum fluctuation properties of spinor field in two-dimensional black holes are studied,and the local charge-current density fluctuations of spinor field in point matter black holes and non-commutative black holes are derived by using the solution of Dirac equation when the gravitational field is perturbed.In Chapter 6,the mapping and quantum motion properties of the Dirac equation in two-dimensional black holes are studied,the Hamiltonian of the modified Rabi model in point matter black hole and non-commutative black hole are obtained,and the modified formulas of motion velocity and acceleration for simulating Dirac particles are derived.The innovative work in this thesis is as follows:1.The falling time of particles in point matter black hole and non-commutative black hole is calculated when the gravitational field is disturbed,the energy density fluctuation formula of scalar field and the local charge current density fluctuation formula of spinor field are derived respectively.2.The Hamiltonian of modified Rabi model in point matter black hole and non-commutative black hole is derived,and the modified expressions of velocity and acceleration for simulating Dirac particles are obtained. |
