Thermodynamic Geometry of Black Holes in the Canonical Ensemble

Abstract

We investigate the thermodynamics and critical phenomena for four dimensional RN-AdS and Kerr-AdS black holes in the canonical ensemble both for the normal and the extended phase space employing the framework of thermodynamic geometry. The thermodynamic scalar curvatures for these black holes characterizes the liquid-gas like first order phase transition analogous to the van der Waals fluids, through the $R$-Crossing Method. It is also shown that the thermodynamic scalar curvatures diverge as a function of the temperature at the critical point.

17 pages Latex, 8 figures

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• Thermodynamic Geometry of AdS Black Holes and Black Holes in a Cavity
• Thermodynamic geometry and interacting microstructures of BTZ black holes
• Ruppeiner Geometry, Reentrant Phase transition and Microstructure of Born-Infeld AdS Black Hole
• Black hole geometrothermodynamics and critical phenomena: a look from Tsallis entropy-based perspective
• Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity
• Ruppeiner Geometry of the RN-AdS Black Hole Using Shadow Formalism
• Thermodynamic Geometry of Black Holes Enclosed by a Cavity in Extended Phase Space
• Thermodynamics of 2+1 dimensional Coulomb-Like Black Holes from Non Linear Electrodynamics with a traceless energy momentum tensor
• Overview of thermodynamic properties for Reissner-Nordstrom-de Sitter spacetime in induced phase space