Thermodynamic geometry of the RN-AdS black hole and non-local observables

TL;DR

This paper explores the connection between the thermodynamic geometry of RN-AdS black holes and non-local observables in boundary field theory, revealing insights into black hole thermodynamics through boundary phenomena.

Contribution

It introduces a universal equation of state for RN-AdS black holes using the cosmological constant and numerically studies the correspondence with boundary non-local observables.

Findings

Thermodynamic properties relate to oscillating behaviors of boundary observables.

Universal equation of state for RN-AdS black holes established.

Thermodynamic geometry can be inferred from boundary field theory.

Abstract

In this paper, we show the relation between the thermodynamic geometry of a four-dimensional Reissner-Nordstrom-AdS (RN-AdS) black hole and non-local observables in boundary field theory. Instead of introducing the critical point associating with the black hole charge to nondimensionalize the thermodynamics parameters, we use the cosmological constant to rescale these variables, so that a universal specific equation of state of the black hole is obtained. Further, the correspondence between thermodynamic properties of the black hole and the oscillating behaviors of the non-local observables has been studied numerically. Our results indicate that the study of the dual field theory will reveal to us the thermodynamic geometry of the AdS black hole.