Van Der Waals Black Hole And Its Geometrothermodynamics

Geometrothermodynamics is a new method to study the thermodynamic prop－erties of black holes and ordinary systems in recent ten years.By this method,we can introduce the corresponding thermodynamic metrics in the phase spaces of the systems,then we turn to studying the geometric properties.This correspondence between them has been verified by a large number of previous works for different thermodynamic systems.And it is universal and consistent with the results obtained by other methods.In the Chapter Ⅱ,we introduce a special kind of asmptotic AdS black hole,which is called the Van der Waals black hole,in the four-dimensional spacetime.Specially the state equation of this black hole is exactly the same as the state equation of Van der Waals fluid when we treat the cosmological constant as the thermodynamie pressure.Different from other methods,the metric is obtained by combining general state equation of AdS black hole and Van der Waals state equation.Therefore,we must check that energy conditions to test it’s physically available.In the Chapter Ⅲ,we analyse the influence of different,values of parameters a and b on the geometrothermodynaic properties of Van der Waals black hole.Through calculation,there is an analoge between the thermodynamic characteris-tics of Van der Waals black hole and Van der Waals fluid.In this way,we can construct a corresponding relation between the black holes and the or dinary ther-modynamic systems.When the state equation reduces to ideal gas state,Van der Waals black hole reduces to Schwarzscliild-AdS black hole,which behaves like ideal gas in thermodynamics.It suggests that the relation has been preserved in this limit case.