Revisiting the thermodynamics of the BTZ black hole with a variable gravitational constant

The thermodynamics of BTZ black holes are revisited with a variable gravitational constant.A new pair of conjugated thermodynamic variables are introduced,including the central charge C and chemical potentialμ.The first law of thermodynamics and the Euler relationship,instead of the Smarr relationship in the extended phase space formalism,are matched perfectly in the proposed formalism.Compatible with the standard extensive thermodynamics of an ordinary system,the black hole mass is verified to be a first order homogeneous function of the related extensive variables,and restores the role of internal energy.In addition,the heat capacity has also resulted in a first order homogeneous function using this formalism,and asymptotic behavior is demonstrated at the high temperature limit.The non-negativity of the heat capacity indicates that the rotating and charged BTZ black holes are thermodynamically stable.

Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space

In this paper,we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space.It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity,the charged AdS black hole also admits a van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume.Based on this,we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework.On the one hand,we give the phase diagram structures of the charged AdS black hole accurately and analytically,which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity.On the other hand,we analyse the thermodynamic curvature of the black hole in two coordinate spaces.The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive.Based on an empirical conclusion under the framework of thermodynamic geometry,we speculate that when the square of charge is treated as an independent thermodynamic quantity,the charged AdS black hole is likely to present a repulsive between its molecules.More importantly,based on the thermodynamic curvature,we obtain a universal exponent at the critical point of phase transition.

A new measure of thermal micro-behavior for the AdS black hole

In spired by the hypothesis of the black hole molecule,with the help of the Hawking temperature,entropy,and the thermodynamic curvature of black holes,we propose a new measure of the relation between the interaction and the thermal motion of molecules of the AdS black hole as a preliminary and coarse-grained description.The proposed measure introduces a dimensi on less ratio to characterize this relation and shows that there is indeed competition between the in teractions of black hole molecules and their thermal motion.For a charged AdS black hole,below the critical dimensionless pressure,there are three transitions between the interaction and thermal motion states.In contrast,above the critical dimensionless pressure,only one transition takes place.For the Schwarzschild-AdS and five-dimensional Gauss-Bonnet AdS black holes,a transition always occurs between the interaction and thermal motion states.

Fine micro-thermal structures for Reissner-Nordström black hole

We solve the condundrum on whether the molecules of the Reissner-Nordström black hole interact through the Ruppeiner thermodynamic geometry,basing our study on the concept of the black hole molecule proposed in[Phys.Rev.Lett.115(2015)111302]and choosing the appropriate extensive variables.Our results show that the Reissner-Nordström black hole is indeed an interaction system that may be dominated by repulsive interaction.More importantly,with the help of a novel quantity,namely the thermal-charge density,we describe the fine micro-thermal structures of the Reissner-Nordström black hole in detail.Three different phases are presented,namely the free,interactive,and balanced phases.The thermal-charge density plays a role similar to the order parameter,and the back hole undergoes a new phase transition between the free phase and interactive phase.The competition between the free phase and interactive phase exists,which leads to extreme behavior of the temperature of the Reissner-Nordström black hole.For the extreme Reissner-Nordström black hole,the entire system is completely in the interactive phase.More importantly,we provide the thermodynamic micro-mechanism for the formation of the naked singularity of the Reissner-Nordström black hole.