The Thermodynamic Relationship between the RN-AdS Black Holes and the RN Black Hole in Canonical Ensemble

Yu-Bo Ma,Li-Chun Zhang,Shuo Cao,Ren Zhao,Jian Liu

doi:10.1155/2017/3812063

Abstract

In this paper, by analyzing the thermodynamic properties of charged AdS black hole and asymptotically flat space-time charged black hole in the vicinity of the critical point, we establish the correspondence between the thermodynamic parameters of asymptotically flat space-time and nonasymptotically flat space-time, based on the equality of black hole horizon area in the two different types of space-time. The relationship between the cavity radius (which is introduced in the study of asymptotically flat space-time charged black holes) and the cosmological constant (which is introduced in the study of nonasymptotically flat space-time) is determined. The establishment of the correspondence between the thermodynamics parameters in two different types of space-time is beneficial to the mutual promotion of different time-space black hole research, which is helpful to understand the thermodynamics and quantum properties of black hole in space-time.

Highlights

Introduction constantΛ could be an independent thermodynamic parameter, and the first law of thermodynamics ofThe AdS black hole solution in four-dimensional spacetime is an accurate black hole solution of the Einstein equation with negative cosmological constant in asymptotic AdS space time [1]
This solution has the same thermodynamic characteristics as the black hole solution in asymptotically flat space-time, i.e., the black hole entropy is equal to a quarter of the event horizon area, while the corresponding thermodynamics quantity satisfies the law of thermodynamics of black hole
The P − V critical properties of AdS black hole was firstly studied in Ref [4], which found that the phase transition and critical behavior of RN-AdS black hole are similar to those of the general van der waalsMaxwell system

Summary

The corresponding reduction quantities are defined as IE

There is no definite value for the radius in our analysis, which provides us the possibility to adjust this parameter to obtain similar thermodynamic properties from the black holes in two different space-time, and derive the relationship between the radius of the cavity and the radius of the black hole r+ or the cosmological constant l. In order to obtain similar thermodynamic properties of the black holes in two different space-time, we ensure that with the change of horizon radius of black hole, the temperature and entropy of the two systems are kept to be equal.

It is straightforward to obtain

Conclusion

The y x curve for