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Boundary Conditions for NHEK through Effective Action Approach
High Energy Physics - Theory · Submitted 14 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed in 0907.0303, and still allow a copy of conformal group as its ASG.
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We study the asymptotic symmetry group(ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed in 1007.1031. By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed in 0907.0303, and still allow a copy of conformal group as its ASG. In the covariant formalism, the asymptotic charges are finite, with the corresponding central charge vanishing. By using the quasi-local charge and introducing a plausible cut-off, we find that the higher order terms of the asymptotic Killing vectors, which could not be determined through the effective action approach, contribute to the central charge as well. We also show that the boundary conditions suggested in 0809.4266 lead to a divergent first order boundary effective action.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the asymptotic symmetry group(ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed in 1007.1031. | contribution 0.90 | 0.90 | 0.06 | asserted 0.97 |
| s1 | By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed in 0907.0303, and still allow a copy of conformal group as its ASG. | result 0.74 | 0.96 | 0.67 | asserted 1.00 |
| s2 | In the covariant formalism, the asymptotic charges are finite, with the corresponding central charge vanishing. | result 1.00 | 0.86 | 0.15 | asserted 1.00 |
| s3 | By using the quasi-local charge and introducing a plausible cut-off, we find that the higher order terms of the asymptotic Killing vectors, which could not be determined through the effective action approach, contribute to the central charge as well. | result 0.90 | 0.95 | 0.18 | asserted 0.99 |
| s4 | We also show that the boundary conditions suggested in 0809.4266 lead to a divergent first order boundary effective action. | result 0.98 | 0.84 | 0.07 | asserted 1.00 |
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The paper
Original abstract
We study the asymptotic symmetry group(ASG) of the near horizon geometry of extreme Kerr black hole through the effective action approach developed in 1007.1031. By requiring a finite boundary effective action, we derive a new set of asymptotic Killing vectors and boundary conditions, which are much more relaxed than the ones proposed in 0907.0303, and still allow a copy of conformal group as its ASG. In the covariant formalism, the asymptotic charges are finite, with the corresponding central charge vanishing. By using the quasi-local charge and introducing a plausible cut-off, we find that the higher order terms of the asymptotic Killing vectors, which could not be determined through the effective action approach, contribute to the central charge as well. We also show that the boundary conditions suggested in 0809.4266 lead to a divergent first order boundary effective action.
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How the literature uses it
3 arXiv papers cite this in 3 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 1 paper
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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
What it cites · 22 sentences without a confident label
Contests 1 paper
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Furthermore our study shows that the boundary conditions suggested in [ref] are in conflict with the finiteness of the boundary effective action.
The Kerr/CFT Correspondence · Introduction · contest 0.77
Uses the method or tool of 4 papers
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Employing the quasi-local charge [ref] defined by using the surface energy momentum tensor, it turns out that our asymptotic Killing vectors ([ref]) give rise to Virasoro algebra with the following central extension term 1/2πi∮dτ∫dθ dϕ 𝒞_m, n(τ,θ,ϕ) , in which 𝒞_m, n(τ,θ,ϕ) = - J ϵ_m(τ)/16 π ( Ω^2 ( Ω Γ' + 4 Γ Ω') ξ^θ_-1 + 2 Γ Ω^3 ξ^r_0 - 4 ( Ω Γ' + Γ Ω') ξ^r_0, θ - 4 Γ Ω ξ^r_0, θθ) - J ϵ_m(τ)/64 πΛ Γ Ω ( 4 Γ^2 Ω^4( ϵ_n”'(τ) + 2 ϵ_n'(τ)+ 2 ξ^r_-1 + 2 ξ^ϕ_-2, ϕ) + 4 Γ Ω^3 ( Ω Γ' + 4 Γ Ω') ξ^θ_-2 - 16 Γ Ω( Ω Γ' + Γ Ω') ξ^r_-1, θ + 16 Γ^2 ( Ω^2 - 1) ξ^r_-1, ϕϕ - 16 Γ^2 Ω^2 ξ^r_-1, θθ + 4 Γ^2 Ω^4 ( 3 ξ^r_0^2 - ξ^r_0, θ^2 - 4 ξ^ϕ_0, τ^2 ) + ( 4 Γ^2 Ω^4 + 16 Γ^2 Ω'^ 2 + 16 Γ^2 Ω Ω” + 16 Γ Ω Γ' Ω' - 8 Γ Ω^3 Γ' Ω' - Ω^4 Γ'^ 2) ξ^θ_-1^2 + 16 Γ Ω( Ω^3 Γ' - 3 Ω Γ' - 3 Γ Ω') ξ^r_0 ξ^r_0, θ + 16 Γ^2 Ω^2 ( Ω^2 - 3) ξ^r_0 ξ^r_0, θθ - 16 Γ Ω( Ω Γ' + Γ Ω') ξ^θ_-1 ξ^θ_-1, θ - 16 Γ^2 Ω^2 ξ^θ_-1 ξ^θ_-1, θθ
Quasilocal Energy and Conserved Charges Derived from the Gravitational Action · Central Charge · 1.00
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Furthermore, adopting the covariant formalism developed by Barnich, Brandt and Compère [ref] , we find that the asymptotic charges $Q[ξ]$ corresponding to ([ref]) and ([ref]) are finite, with the trivial symmetry transformations ξ_tr = (1/r^3)_τ +(ξ^r_0(τ,θ)+(1/r))_r +(ξ^θ_-1(τ,θ)1/r+(1/r^2))_θ+(ξ^ϕ_0(τ)+(1/r^2))_ϕgive rise to vanishing charges.
Surface charge algebra in gauge theories and thermodynamic integrability · Asymptotic Killing Vectors for NHEK · 0.99
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Furthermore, adopting the covariant formalism developed by Barnich, Brandt and Compère [ref] , we find that the asymptotic charges $Q[ξ]$ corresponding to ([ref]) and ([ref]) are finite, with the trivial symmetry transformations ξ_tr = (1/r^3)_τ +(ξ^r_0(τ,θ)+(1/r))_r +(ξ^θ_-1(τ,θ)1/r+(1/r^2))_θ+(ξ^ϕ_0(τ)+(1/r^2))_ϕgive rise to vanishing charges.
Covariant theory of asymptotic symmetries, conservation laws and central charges · Asymptotic Killing Vectors for NHEK · 0.99
Compares with 1 paper
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Although we fail to find the boundary conditions admitting two copies of Virasoro algebras, we do find a set of new boundary conditions, which are more relaxed compared to the boundary conditions proposed in [ref] but still allows one copy of conformal group as its ASG.
Another Realization of Kerr/CFT Correspondence · Introduction · 0.99
Cites as background 1 paper
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In the derivation of the ASG of NHEK, a set of boundary conditions was proposed in [ref] .
The Kerr/CFT Correspondence · Introduction · 0.97
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