Black Hole Thermodynamics And Chaos In Extended Phase Space

In recent years,the thermodynamics of black hole in Ad S spacetime has gained more and more attention.It has been found that charged Ad S black holes have critical behavior similar to van der Waals fluid,and that reentrant phase transition occurs in six and higher-dimensional spinning black holes and four-dimensional Born-Infeld-Ad S black holes.These researches greatly expand our understanding of black hole thermodynamics,which makes scholars pay more attention to the thermodynamic properties of black holes inescapable when they develop the black hole theory.This thesis first focus on the concept of black hole in the sense of modern physics,in which black hole is a special spacetime region that can be described by a metric.Theoretically,people can only enter into it but never go out,and there is a singularity in the center of the region.These peculiar properties make it very different from other celestial bodies,including white dwarf stars and pulsars.In the study of black hole theory,black hole thermodynamics is an important field.In this thesis,we study the black hole thermodynamics in extended phase space,in which the negative cosmological constant is interpreted as the thermodynamic pressure.In the extended phase space,the thermodynamic behavior of black holes is very similar to that of ordinary systems.This thesis focuses on the similarity between the charged Ad S black holes and van der Waals flow.On this basis,a type of black hole with special electromagnetic field,Born-Infeld field,has attracted the author's attention.The Born-Infeld-Ad S black hole has complicated phase structures and transitions,including a large-small black hole transition in four dimensions which is similar to the gas-liquid phase transition of van der Waals liquid.Therefore,basing on the study of chaos in charged Ad S black hole regime,this paper explores the chaotic behavior of Born-Infeld-Ad S black hole regime.Melnikov function method,widely used in chaos theory,is proved to be applicable in Van der Waals fluid system in 1980 s.With this method,we found that the two parameters of Born-Infeld-Ad S black hole,charge Q and Born-Infeld parameter b,which both appear in the first law of the black hole thermodynamics,,can both make the black hole system more prone to chaos.