The Thermodynamics Of DBI Black Hole In Anti-de Sitter Space Time

The new composition of universe material has changed people's old cosmology view. It has left a lot of suspense for the people to explore the universe. People are promoting the new thinking of the exploration of the universe. Dark matter and dark energy have become one of the most active areas in modern physics and cosmology. Black holes as models of dark matter and dark energy have important value to be studied. According to the famous theorem-no hair theorem of the black hole, and in view of the descriptions of the physical laws of thermodynamics which are independent on the structural details of the system, physicists identify a black hole with a thermodynamic system and set up thermodynamics of black hole. Recently, the thermodynamics of different kinds of black holes attract physicists'attention. Through the study of the black hole thermodynamics, people hope to give a deeper understanding of the universe.This paper contains three parts. In the first part: we give the general function of metric and action of DBI-AdS black hole with the predecessors'results. Learning the method from the reference [5] which Harry and other physicists applied to obtain the thermodynamics of a black hole, we obtain the metric solutions of DBI-AdS black hole. Based on the metric solutions, we derive out the expression of the DBI-AdS action.We devotes to discuss the thermodynamics of DBI-AdS black hole in the second part. According to the relationship between the giant partition function and the Euclidian action function, we obtain the explicit expressions of some thermodynamic quantities, and investigate the thermodynamics character of DBI-AdS black hole. The stability of the black hole is also discussed.How to solve Dirac field in curved space time is an important problem. Black hole with mass and charge (Kerr-Newman black hole) has been discussed in [63]. In part three, we try to study the solution of Dirac equation in DBI-AdS black hole background with mass and charge. This will be continued in future.