Topological black holes in pure Gauss-Bonnet gravity and phase transitions

Abstract

We study charged, static, topological black holes in pure Gauss-Bonnet gravity in asymptotically AdS space. As in general relativity, the theory possesses a unique nondegenerate AdS vacuum. It also admits charged black hole solutions which asymptotically behave as the Reissner-Nordström AdS black hole. We discuss black hole thermodynamics of these black holes. Then we study phase transitions in a dual quantum field theory in four dimensions, with the Stückelberg scalar field as an order parameter. We find in the probe limit that the black hole can develop hair below some critical temperature, which suggests a phase transition. Depending on the scalar coupling constants, the phase transition can be first or second order. Analysis of the free energy reveals that, comparing the two solutions, the hairy state is energetically favorable, thus a phase transition will occur in a dual field theory.

28 pages, 3 figures; V2:References modified; Probe limit added; V3: Minor correction, Published version

References in corpus (19)

• Building an AdS/CFT superconductor
• Lectures on Holographic Superfluidity and Superconductivity
• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• The Lovelock Black Holes
• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
• Black Holes in Pure Lovelock Gravities
• Universal regularization prescription for Lovelock AdS gravity
• Gauss-Bonnet Holographic Superconductors
• Vacuum energy in Einstein-Gauss-Bonnet AdS gravity
• Counterterms in Dimensionally Continued AdS Gravity
• On black strings & branes in Lovelock gravity
• Exact Gravity Dual of a Gapless Superconductor
• Simple compactifications and Black p-branes in Gauss-Bonnet and Lovelock Theories
• Phases of Holographic Superconductors in an External Magnetic Field
• Holographic Superconductors in Quasi-topological Gravity
• Universal Kounterterms in Lovelock AdS gravity
• Conformal Mass in AdS gravity
• Black hole solutions in Chern-Simons AdS supergravity
• Holographic phase transition and Quasinormal modes in Lovelock gravity

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• Dynamical structure of Pure Lovelock gravity
• Pure Lovelock gravity and Chern-Simons theory
• Lovelock gravities from Born-Infeld gravity theory
• $P-v$ criticality of a specific black hole in $f(R)$ gravity coupled with Yang-Mills field
• Pure Lovelock black hole in the dimension, $d=3N+1$, is stable
• Null paths on a toroidal topological black hole in conformalWeyl gravity
• Charged strange star model in Tolman-Kuchowicz spacetime in the background of 5D Einstein-Maxwell-Gauss-Bonnet gravity
• Topological Interpretation of Black Hole Phase Transition in Gauss-Bonnet Gravity
• Thermodynamic extended phase space and $P-V$ criticality of black holes at Pure Lovelock gravity
• Gravitational Decoupling algorithm modifies the value of the conserved charges and thermodynamics properties in Lovelock Unique Vacuum theory
• Five-dimensional compact stars in Einstein-Gauss-Bonnet gravity
• Higher-curvature generalization of Eguchi-Hanson spaces
• First-order Lagrangian and Hamiltonian of Lovelock gravity