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

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-Nordström 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.

The Hookean Law of Black Holes and Fragmentation: Insights from Maximum Force Conjecture and Ruppeiner Geometry

“…In addition, we can define a "force" by taking the ratio F 2 := J 2 /S 2 , where J is the angular momentum and S the Bekenstein-Hawking entropy of the black hole. These two thermodynamical variables can be used to define the so-called Ruppeiner geometry [13] -a two-dimensional Riemannian metric in thermodynamic phase space -which has recently gained some attention in the context of black hole microstructure [14][15][16][17][18][19][20][21] and applications to black hole shadows [22][23][24]. Interestingly, the region in the thermodynamic phase space with positive Ruppeiner scalar curvature is marked by the boundary F 2 = 1 As pointed out by Emparan and Myers, at this point the temperature of the black hole starts to behave like a black brane instead of a Kerr-type black hole.…”