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Holographic superconductor in the exact hairy black hole
High Energy Physics - Theory · Submitted 6 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim However, this transition unlikely occur.
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The abstract, sentence by sentence
We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor. For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordstr\"om-AdS (HRNAdS) black holes. However, this transition unlikely occur. As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature. The presence of charge destroys the condensates around the zero temperature, which is in accord with the thermodynamic analysis of the CMTZ black hole.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor. | contribution 0.70 | 0.63 | 0.06 | asserted 0.99 |
| s1 | For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordstr\"om-AdS (HRNAdS) black holes. | method 0.50 | 0.78 | 0.05 | asserted 0.92 |
| s2 | However, this transition unlikely occur. | result 0.92 | 0.54 | 0.35 | hedged possibility 0.79 |
| s3 | As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature. | contribution 0.80 | 0.92 | 0.24 | asserted 1.00 |
| s4 | The presence of charge destroys the condensates around the zero temperature, which is in accord with the thermodynamic analysis of the CMTZ black hole. | result 0.88 | 0.75 | 0.29 | asserted 0.94 |
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The paper
Original abstract
We study the charged black hole of hyperbolic horizon with scalar hair (charged Martinez-Troncoso-Zanelli: CMTZ black hole) as a model of analytic hairy black hole for holographic superconductor. For this purpose, we investigate the second order phase transition between CMTZ and hyperbolic Reissner-Nordstr\"om-AdS (HRNAdS) black holes. However, this transition unlikely occur. As an analytic treatment for holographic superconductor, we develop superconductor in the bulk and superfluidity on the boundary using the CMTZ black hole below the critical temperature. The presence of charge destroys the condensates around the zero temperature, which is in accord with the thermodynamic analysis of the CMTZ black hole.
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How the literature uses it
6 arXiv papers cite this in 7 sentences
Papers citing it · 3 sentences without a confident label
Contests it 1 paper
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However, the analysis in [ref] is not clear for lack of a thermodynamical ensemble.
Phase transitions in charged topological black holes dressed with a scalar hair · Introduction · contest 0.76
Compares with it 2 papers
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A similar case was found in the charged MTZ black hole [ref]
Phase transitions for the Lifshitz black holes · Lifshitz brane and black brane · 0.94
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A similar case was found in the charged MTZ black hole [ref]
Quasinormal frequencies and thermodynamic quantities for the Lifshitz black holes · Einstein-scalar-Maxwell theory · 0.91
Cites it as background 1 paper
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The s-wave holographic superconductors were extended and investigated by many authors [ref] .
Analysis of s-wave, p-wave and d-wave holographic superconductors in Ho\v{r}ava-Lifshitz gravity · Introduction · 0.89
What it cites · 32 sentences without a confident label
Uses the method or tool of 2 papers
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Here we observe a linear relation between temperature and heat capacity [equation] with the entropy for the MTZ black hole [equation] However, since the conformal coupling term appears in the action, the entropy should be obtained by making use of the Euclidean action approach [ref] and the Wald method [ref] as [equation] where an effective Newtonian constant at the event horizon is given by [equation] The positivity of entropy $S_M ≥0$ requires a bound [equation] It requires lower bounds for being the positive entropy.
Thermodynamical properties of hairy black holes in n spacetimes dimensions · CMTZ black holes · 0.84
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Here we observe a linear relation between temperature and heat capacity [equation] with the entropy for the MTZ black hole [equation] However, since the conformal coupling term appears in the action, the entropy should be obtained by making use of the Euclidean action approach [ref] and the Wald method [ref] as [equation] where an effective Newtonian constant at the event horizon is given by [equation] The positivity of entropy $S_M ≥0$ requires a bound [equation] It requires lower bounds for being the positive entropy.
Topological black holes dressed with a conformally coupled scalar field and electric charge · CMTZ black holes · 0.84
Compares with 3 papers
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Moreover, near the critical temperature, two condensate behave like [equation] Comparing these critical exponents with those of the MTZ black hole [ref] , the black hole charge $q$ which corresponds to the charge density on the boundary field theory decreases the critical exponents $c_i$ defined by $< O_i > ≃( 1 - T_M/T_0 )^c_i$: $c_1=1 →0$ and $c_2=2 →1$.
Exact Gravity Dual of a Gapless Superconductor · Gapless superconductivity · 0.81
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We observe that similar results for the conductivity depending on the charge density were found in the Horowitz-Roberts model [ref] and Ref. [ref] .
Zero Temperature Limit of Holographic Superconductors · Discussion · 1.00
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We observe that similar results for the conductivity depending on the charge density were found in the Horowitz-Roberts model [ref] and Ref. [ref] .
Holographic conductivity of zero temperature superconductors · Discussion · 1.00
Cites as background 3 papers
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Fortunately, the charged MTZ (CMTZ) black hole was found with scalar hair when the coefficient $α$ of $ϕ^4$-term is between 0 and $2πG/3l^2$ [ref] , where the upper bound corresponds to the MTZ black hole [ref] and the lower bound is not allowed.
Topological black holes dressed with a conformally coupled scalar field and electric charge · Introduction · 0.81
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In order to understand the role of scalar and its potential well, it would be better to start with the conformally coupled action [ref] I_4[g,ϕ,A_μ]= ∫d^4x√(-g)[R-2Λ/16 πG-(D_μϕ)^*(D^μϕ)-1/6R ϕϕ^*-4α(ϕϕ^*)^2-1/16πF^μνF_μν] , where a conformally charged coupled scalar $ϕ$ appears with a conventional potential term $α(ϕϕ^*)^2$ and [equation] We note the mass dimensions of $[ϕ]=[ϕ^*]=[A_μ]=1$.
Exact Gravity Dual of a Gapless Superconductor · CMTZ black holes · 0.83
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Actually, to study the first order phase transition as the Hawking-Page transition [ref] , one requires the heat capacity and free energy because it describes a phase transition from a hot gas, via small unstable black hole with negative heat capacity, to large stable black hole with positive heat capacity in AdS$_4$ spacetimes [ref] .
Thermodynamics and phase transitions in the Born-Infeld-anti-de Sitter black holes · CMTZ black holes · 0.85
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