Ruppeiner Geometry of the RN-AdS Black Hole Using Shadow Formalism

TL;DR

This paper explores how the shadow radius of a Reissner-Nordström AdS black hole relates to its Ruppeiner geometry, revealing phase transitions and microstructure insights through shadow observations.

Contribution

It introduces a novel approach linking shadow radius to Ruppeiner geometry, providing a new observational method to study black hole phase structure.

Findings

Shadow radius correlates with phase transitions.

Ruppeiner curvature reveals microstructure details.

Shadow formalism offers observational insights into black hole thermodynamics.

Abstract

The connection between the shadow radius and the Ruppeiner geometry of a charged static spherically symmetric black hole is investigated. The normalized curvature scalar is adopted, and its close relation to the Van der Waals-like and Hawking-Page phase transition of Reissner-Nordstr\"{o}m AdS black hole is studied. The results show that the shadow radius is a useful tool to reveal the correct information of the phase structure and the underlying microstructure of the black hole, which opens a new window to investigate the strong gravity system from the observational point of view.