Blackhole And Thermodynamics Phase Transition

This paper investigated the horizons and geodesic of particle in RN?A?dS spacetime surrounded by quintessence[Q-RN?A?dS],the first order phase transition of RN AdS blackhole as well as the blackhole thermodynamics and phase transition in Grumiller spacetime.A new method is introduced to study the classification of spacetime,and spacetime horizon and timelike geodesics are investigated in the background spacetime of Reissner-Nordstrom?anti-?de Sitter black hole surrounded by the quintessence.We find that,for Q-RN AdS metric,there are two types of black holes:two horizons and four horizons.In a black hole spacetime of two horizons,the angular procession of the aphelion per revolution increases with the increase of the quintessence parameter_qr;While the number of aphelion per revolution increases with the decrease of the quintessence equation of state parameterw_q.This shows that the quintessence parameters_qr and_qwcan be determined by measuring the angular precession and number of aphelion per revolution,respectively.For Q-RN dS metric there are two cases:one horizon and three horizons.The Q-RN dS Metric of one horizon describes the de Sitter-like spacetime,which has a naked singularity at r?28?0.It's interesting to note that any particle never reaches the singularity,since the effective potential is infinite at the point.On the other hand,the quintessence has no significant on the geodesics in de Sitter-like spacetime.It's worth pointing out that there are no bound states for the Q-RN AdS spacetime with four horizons and the Q-RN dS spacetime with three horizons.The first order phase transiton?PT?of RN AdS blackhole was studied based on the parameter solutions in coexistence line.By parameter solutions,some quantities was obtained and related phase diagrams was plotted.When parameter w is small,the behavior of the phase diagrams is similar to conventional vdW gas-liquid phase transition;If the wis increasing?away from critical point of first order PT?,two strange curves appear on P-T coexistence line,which is different to vdW fluid.On one of the curves,with the increase of w,the temperature and pressure are increased,and the Gibbs function and order parameter are decreased.On the other one of curves,with increased w?P-T coexistence line approaches to origin point?,the pressure,temperature and order parameter are decreased,and the Gibbs function is increased.Furthermore,the Gibbs function and average number density of molecules are investigated,their series expansion are identical withinO(w^5/2),actually,it shows by figure that they split distinctly atw?25?10¹⁰.Also,the critical exponents of RN AdS blackhole,??28?0,??28?1₂,^??28?1,??28?3,were obtained by the expansion of related quantities.The first law and general Smarr relation of blackhole in Grumiller spacetime were constructed by scaling theory,where the cosmological constant was treated as pressure and surface gravity was treated as temperature,the surface area and volume of blackhole were treated as entropy and thermodynamic volume,respectively.It was also found that the conjugate variable of Rindler acceleration term in Grumiller is related to the total number of molecules within the surface of blackhole,thus Rindler acceleration could be treated as chemical potential of blackhole.The blackhole PTs were also studied,including Hawking-Page PT and the second order Erenfest PT which happens between stable phase and unstable phase.