Physical Properties For Bose Condensed Matter On The Black Hole Background And Analogical Gravitation Research

In this thesis,the physical properties of Bose condensates in?2+1?and?3+1?dimensional black holes background are studied,and the acoustic black hole model in?1+1?dimensional analogical gravity theory is also studied.In Chapter 1,the history of Bose-Einstein condensation and analogous gravitation are briefly introduced,as well as the observation status of gravitational waves from black holes.In Chapter 2,the holographic fluctuations of condensed matter under the BTZ black hole and topological black hole background according to the G-P equation with boundary perturbation in AdS₃/CFT₂ space-time are calculated.In Chapter 3,the mathematical and physical properties of the O?N?vector field condensation model under the Kerr-BTZ black hole background are studied by using the functional integral method in quantum field theory,the free energy of the condensation field on the d-dimensional sphere is also derived from the large N expansion technique.In chapter 4,the radiation frequencies of the gravitational waves from superfluid axions around Kerr-Newmann and Kerr-Sen black holes are calculated respectively according to the G-P equation under the rotating black hole background.In chapter 5,the two-dimensional acoustical black hole metric is deduced by using the canonical transformation and functional integration method,then the effective mass of phonon,Hawking temperature,fluid velocity at vacuum point and decay probability of phonon Higgs vacuum in different 2-D gravitational models are calculated respectively.The innovative works in this thesis are as follows:1.The convergence and thermodynamic stability of the O?N?vector field condensation model under Kerr-BTZ black hole background are proved by functional integration method.2.The gravitational wave radiation frequencies of superfluid axions around the Kerr-Newmann and Kerr-Sen black holes are calculated for the first time.3.The effective mass of phonon,Hawking temperature,fluid velocity at vacuum point and decay probability of phonon Higgs vacuum corresponding to different 2-D gravitational models in acoustic black holes are calculated for the first time.