Thermodynamics And Phase Transitions Of 4-dimentional RN-Taub-NUT-AdS Spacetime

In classical black hole theory,black holes lose every other information they held before the formation except matter,angular momentum and charge.This is known as “no-hair theorem”.Later Hawking discovered that black holes radiate like a black body,this theory showed thermodynamic properties of black holes and manifested the connections between quantum theory,thermodynamics and gravity theory.The research on black hole thermodynamic properties showed rich phase transition behaviors of AdS black holes.Especially,the research on RN-AdS black hole,in extended thermodynamic phase space,demonstrated a first order phase transition the same as that of Van der Waals fluids' liquid-gas system.Taub-NUT-AdS spacetime is a simple non-radiate exact solution of Einstein field equation and considered as a possible black hole solution.In this paper,we extend the black hole phase transition analysis to RN-Taub-NUT-AdS spacetime,analyzing the effect of NUT charge on the phase transitions.We consider the fourdimentional RN-Taub-NUT-AdS spacetime thermodynamics with nonzero cosmological constant and electric charge.NUT parameter is interpreted as the thermodynamic multihair(rotation-like,electromagnetic charge-like or magnetic mass-like)in the extended thermodynamic phase space.We focus on the effects of the NUT parameter on the phase transitions and the thermodynamical analogy to the classical Van der Waals liquid-gas system.We find that when the NUT parameter is vanishingly small,the analogy to the Van der Waals' liquid/gas phase transition is valid,irrespective of the multihair characteristics of the NUT parameter.However,as the NUT parameter increase,such analogy to the Van der Waals system will be gradually broken.We find that there is an upper bound on the value of the NUT parameter related to electric charge,beyond which the corresponding inflection point is not a thermodynamic critical point any more.And we find that the thermodynamic trihair interpretation of the NUT parameter would admit a little larger upper bound than the thermodynamic bihair interpretation.Particularly,the behavior of phase transitions becomes quite rich in the case of the thermodynamic bihair interpretation of the NUT parameter.Lastly,for a large NUT parameter,while only the first order phase transition happens in the case of the thermodynamic trihair interpretation,there are frequent occurrences of the zeroth order phase transition in the case of the thermodynamic bihair interpretation.