The thermodynamic relationship between the RN-AdS black holes and the RN black hole in canonical ensemble

TL;DR

This paper explores the thermodynamic relationship between Reissner-Nordström Anti-de Sitter (RN-AdS) black holes and RN black holes in flat space, establishing a correspondence between their parameters near critical points to enhance understanding of black hole thermodynamics.

Contribution

It introduces a novel correspondence between thermodynamic parameters of asymptotically flat and AdS black holes based on horizon area equality, linking cavity radius and cosmological constant.

Findings

Established thermodynamic parameter correspondence between different space-times.

Linked cavity radius to cosmological constant near critical points.

Enhanced understanding of black hole thermodynamics and quantum properties.

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 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 space-time is beneficial to the mutual promotion of different time-space black hole research, which is helpful to understand the thermodynamics and quantumproperties of black hole in space-time.