Thermodynamics Of D-dimension Bardeen Einstein-Gauss-Bonnet AdS Black Hole

Black hole is object whose curvature in space-time is so large that light cannot escape.In the traditional sense,it can absorbs all substances like ultimate sponge without release any substances,so we cannot directly observe the black hole.We can only know its existence through indirect methods,i.e.observing its impact on other things.The research on the thermodynamics of black hole originated from the definition of the entropy and temperature of black hole by Hawking and Bekenstein.The entropy of black hole is a measure of the inside of black hole,Such information cannot be obtained by external observation,and the area and entropy of black hole tend to increase irreversibly.The thermodynamics of black hole has been developed for nearly half a century,and over the past few years,a great deal of studies showed that there are some fundamental connections between thermodynamics and quantum theory,which has evolved into a branch called-black hole thermodynamics.In this thesis,we study the thermodynamic properties of black holes in the background of D-dimensional Bardeen Einstein-Gauss-Bonnet(EGB)AdS black hole and the thermal engine efficiency of black hole in this background.In chapter I,we describe the research history and development status of black hole thermodynamics,in detail.Including classical black hole thermodynamic prop-erties,black hole entropy,hawking radiation,generalized second law and so on.We also introduce the method of calculating the entropy of black hole in detail.We investigate the extended black hole thermodynamics in the context of a black hole with a cosmic constant,and the treatment of the cosmic constant in the extend-ed black hole thermodynamics,and the first law of thermodynamics that changes accordingly.Finally,we study the principle and engine efficiency of black holes as working substance of heat engines.In chapter ?,we review the space-time of D-dimensions Bardeen Einstein-Gauss-Bonnet(EGB)AdS black,and investigate the P-V critical state and the state equation of D-dimensions Bardeen EGB AdS black hole.We study the critical characteristics of P-V in this black hole background in detail.Then comparing it with the Van der Waals(VdW)system,we find that there have some similar ther-modynamic characteristics between our black hole background and VdW system.In chapter ?,we systematically study the heat engine by takeing black hole as working substance of the heat engine,and compare the engine efficiency with that of the famous Carnot heat engine.The heat engine efficiency change with Bardeen parameter and Gauss-Bonnet parameter are discussed,respectively.By analyzing the change of ratio between the heat engine efficiency and the Carnot heat engine efficiency ?/?c,we prove that the entropy change coincided with the second law of thermodynamics.