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A Near Horizon CFT Dual for Kerr-Newman-$AdS$
High Energy Physics - Theory · Submitted 8 Sep 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that the near horizon regime of a Kerr-Newman-$AdS$ (KN$AdS$) black hole, given by its two dimensional analogue $a la$ Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT).
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The abstract, sentence by sentence
We show that the near horizon regime of a Kerr-Newman-$AdS$ (KN$AdS$) black hole, given by its two dimensional analogue $a la$ Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence (2009 Phys. Rev. D 80, 124008) in the appropriate limits. We also compute the Hawking temperature of the KN$AdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We show that the near horizon regime of a Kerr-Newman-$AdS$ (KN$AdS$) black hole, given by its two dimensional analogue $a la$ Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). | result 0.77 | 0.89 | 0.88 | asserted 1.00 |
| s1 | The s-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. | result 0.98 | 0.88 | 0.27 | asserted 1.00 |
| s2 | Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence (2009 Phys. Rev. D 80, 124008) in the appropriate limits. | result 0.85 | 0.81 | 0.09 | asserted 0.99 |
| s3 | We also compute the Hawking temperature of the KN$AdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter. | contribution 0.46 | 0.94 | 0.07 | asserted 1.00 |
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The paper
Original abstract
We show that the near horizon regime of a Kerr-Newman-$AdS$ (KN$AdS$) black hole, given by its two dimensional analogue $a la$ Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence (2009 Phys. Rev. D 80, 124008) in the appropriate limits. We also compute the Hawking temperature of the KN$AdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter.
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How the literature uses it
6 arXiv papers cite this in 19 sentences
Papers citing it · 10 sentences without a confident label
Builds on it 2 papers
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This method was then extended to study the 4D Kerr-Newman-AdS black hole [ref] .
Thermodynamics of nonspherical black holes from Liouville theory · Introduction · 0.84
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To conclude, we have analyzed quantum near-extremal Kerr black hole properties in the near horizon regime via the construction of an $AdS_2/CFT_1$ correspondence of the $gnNHEK$ metric, as outlined in Table [ref], and extending our previous analysis [ref] to a new spacetime.
Near-Extremal Kerr AdS2xS2 Solution and Black-Hole/Near-Horizion-CFT Duality · Conclusion and Comments · 0.95
Uses its method or tool 2 papers
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We will do this within an $AdS_2/CFT_1$ correspondence by performing a RW two dimensional reduction of the $near-NHEK$ geometry in a specific finite mass gauge following similar constructions as found in [ref] .
Near-Extremal Kerr AdS2xS2 Solution and Black-Hole/Near-Horizion-CFT Duality · Holographic Black Hole Entropy · 0.91
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Our computational construction mirrors that of [ref] , where the near horizon isotropy is exploited to dimensionally reduce physics to two dimensions a la Robinson and Wilczek [ref] .
Near-Extremal Black Hole Thermodynamics from AdS2/CFT1 Correspondence in The Low Energy Limit of 4D Heterotic String Theory · Introduction · 0.95
Compares with it 1 paper
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In addition, our derived zero-mode in eq:cre is in accordance with [ref] and relates to the irreducible mass of its black hole dual via: The lowest Virasoro eigen-mode of a quantum $CFT$ is proportional to the irreducible mass of its black hole dual via the form [equation] This may be a general statement with a large avenue of application, though we are not aware of a rigorous proof at this time.
Near-Extremal Kerr AdS2xS2 Solution and Black-Hole/Near-Horizion-CFT Duality · $AdS_2/CFT_1$ and Entropy of Near Extremal Kerr · 0.88
Cites it as background 3 papers
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The fact that quantum gravity may be dual to a $CFT$ [ref] has spawned a surge, led by Strominger [ref] , Carlip [ref] and Park [ref] , in applying $CFT$ techniques to compute Bekenstein-Hawking Entropy of various black holes [ref] .
Near-Extremal Kerr AdS2xS2 Solution and Black-Hole/Near-Horizion-CFT Duality · Holographic Black Hole Entropy · 0.98
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Since the successful description of the holographic duality between the geometry near the horizon of extremal Kerr black hole and the conformal field theory [ref] , there have been many studies for the holographic duality in various black holes [ref] .
Nonextremal Kerr/CFT on a stretched horizon · Introduction · 0.99
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Note that the 4D Kerr-Newman-AdS black hole has been studied in [ref] .
Thermodynamics of nonspherical black holes from Liouville theory · Conclusion · 0.81
What it cites · 50 sentences without a confident label
Builds on 1 paper
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To conclude, we have analyzed quantum black hole properties in the near horizon regime via CFT techniques, extending the analysis of [ref] to the more general KN$AdS$ spacetime.
Entropy and Temperature From Black-Hole/Near-Horizon-CFT Duality · Conclusion · 0.99
Compares with 1 paper
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Taking the limit of eq:center to Kerr and to extremality yields [equation] which is the same value of the left central charge obtained in the Kerr/CFT correspondence [ref] , further strengthening the proposal of GHSS.
The Kerr/CFT Correspondence · Entropy · 0.94
Cites as support 6 papers
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There exists strong evidence [ref] , that in the near horizon this CFT takes the form of Liouville Theory [equation] with effective dimensionless coupling proportional to: [equation] where the numerator originates from the dimensional reduction procedure and the denominator is a remnant of the parent classical gravitational theory (general relativity).
Entropy and Temperature From Black-Hole/Near-Horizon-CFT Duality · Near Horizon Geometry · 0.99
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There exists strong evidence [ref] , that in the near horizon this CFT takes the form of Liouville Theory [equation] with effective dimensionless coupling proportional to: [equation] where the numerator originates from the dimensional reduction procedure and the denominator is a remnant of the parent classical gravitational theory (general relativity).
Liouville Lost, Liouville Regained: Central Charge in a Dynamical Background · Near Horizon Geometry · 0.99
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There exists strong evidence [ref] , that in the near horizon this CFT takes the form of Liouville Theory [equation] with effective dimensionless coupling proportional to: [equation] where the numerator originates from the dimensional reduction procedure and the denominator is a remnant of the parent classical gravitational theory (general relativity).
Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole · Near Horizon Geometry · 0.99
Cites as background 14 papers
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For the case where $D=2$ the effective action is given by the Polyakov Action [ref] [equation] which has shown to play an important roll for computing quantum gravitational quantities near black hole horizons [ref] and exhibits a unique relationship to conformal algebras [ref] .
Anomalies, Hawking Radiations and Regularity in Rotating Black Holes · Introduction · 0.85
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For the case where $D=2$ the effective action is given by the Polyakov Action [ref] [equation] which has shown to play an important roll for computing quantum gravitational quantities near black hole horizons [ref] and exhibits a unique relationship to conformal algebras [ref] .
Hawking Radiation from Rotating Black Holes and Gravitational Anomalies · Introduction · 0.85
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For the case where $D=2$ the effective action is given by the Polyakov Action [ref] [equation] which has shown to play an important roll for computing quantum gravitational quantities near black hole horizons [ref] and exhibits a unique relationship to conformal algebras [ref] .
Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole · Introduction · 0.85
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