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arXiv 0809.4266hep-thastro-phgr-qc
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Kerr/CFT通信

The Kerr/CFT Correspondence

Monica Guica, Thomas Hartman, Wei Song, Andrew Strominger

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21 pages, no figures
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摘要：

研究了极端Kerr黑洞（其角动量和质量关系为J= GM ^2）视界附近区域的量子引力。证明了一致边界条件的存在，使得渐近对称生成元构成中心荷c_L= 12 J/ \hbar的维拉索罗代数的一个副本.这意味着近视界量子态可以与二维共形场论（CFT）的（手征的一半）量子态相一致。此外，在极限情况下，Frolov-Thorne真空态约化为一个热密度矩阵，其无量纲温度TL =1/2π，共轭能量由维拉索罗代数的零模生成元L0给出.假设么正性，Cardy公式给出了CFT的微观熵S_{micro} =2πJ / \hbar，它再现了宏观的贝肯斯坦-霍金熵S_{macro} =面积/ 4 \hbar G。结果适用于任何一致的酉量子引力理论与克尔解决方案。因此我们推测极端Kerr黑洞与具有中心荷c_L= 12 J/ \hbar的手征二维共形场论是全息对偶的，特别是近极端黑洞GRS 1915+105与具有c_L \sim 2 \times 10^{79}的CFT是近似对偶的。

英文摘要：

Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM^2) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c_L=12J / \hbar. This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T_L=1/2πand conjugate energy given by the zero mode generator, L_0, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S_{micro}=2πJ / \hbar for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S_{macro}=Area / 4\hbar G. The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c_L=12J / \hbar, and in particular that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c_L \sim 2 \times 10^{79}.

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