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

This paper studies the thermodynamic geometry of the Reissner–Nordström-anti-de Sitter (RN-AdS) black hole via detection of the non-local observables in the dual field theory, including the entanglement entropy and equal-time two-point correlation function. With the dimensional analysis, we construct the principle of corresponding states of black hole thermodynamics. As a result, our findings can be applied to black holes with different AdS backgrounds. In this sense, the probe of the thermodynamic geometry of the RN-AdS black hole though the non-local observables in dual field theory has been confirmed numerically.