Ruppeiner curvature along a renormalization group flow

Abstract

We report on an investigation of Ruppeiner curvature $R_U$ for $(d+1)$-dimensional hyperbolic black holes in anti-de Sitter spacetimes and its connection with Renormalization Group (RG) flows in the dual d-dimensional conformal field theories (CFTs) in Minkowski spacetimes. A repulsive type interaction among microstructures is found, which is weaker for positive mass black holes and grows stronger for negative mass black holes at low temperatures. In particular, we show that $R_U$ evaluated along a zero mass curve is a universal constant, depending only on the dimension of space-time. The extremal black holes are pointed out to have a positive Ruppeiner curvature irrespective of their horizon topology.

v3:6 pages,3 figures; substantially revised version, to appear in PLB

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• Thermodynamics curvature in phase transitions for AdS black hole
• Thermodynamic Geometry of Black Holes Enclosed by a Cavity in Extended Phase Space
• Static spheres and Aschenbach effect for black holes in massive gravity
• Microstructure of Charged AdS Black Hole with Minimal Length Effects
• Topological charge and black hole photon spheres in massive gravity