Thermodynamic phase transition and winding number for the third-order Lovelock black hole

Phase transition is important for understanding the nature and evolution of the black hole thermodynamic system.In this study,we predicted the phase transition of the third-order Lovelock black hole using the winding numbers in complex analysis,and qualitatively validated this prediction by the generalized free energy.For the 7<d<12-dimensional black holes in hyperbolic topology and the 7-dimensional black hole in spherical topology,the winding number obtained is three,which indicates that the system undergoes first-order and second-order phase transitions.For the 7<d<12-dimensional black holes in spherical topology,the winding number is four,and two scenarios of phase transitions exist,one involving a purely second-order phase transition and the other involving simultaneous first-order and second-order phase transitions.This result further deepens the research on black hole phase transitions using the complex analysis.

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.

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.

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.