November 26, 2024 | Monica Guica†, Thomas Hartman§, Wei Song§‡, and Andrew Strominger§
The paper explores the holographic correspondence between quantum gravity near the horizon of an extreme Kerr black hole and a two-dimensional conformal field theory (CFT). The authors show that consistent boundary conditions exist, leading to the Virasoro algebra with a central charge \( c_L = \frac{12J}{\hbar} \). This implies that the near-horizon quantum states can be identified with those of a chiral half of a two-dimensional CFT. In the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with a dimensionless temperature \( T_L = \frac{1}{2\pi} \) and conjugate energy given by the zero mode generator \( L_0 \) of the Virasoro algebra. Assuming unitarity, the Cardy formula gives a microscopic entropy \( S_{\text{micro}} = \frac{2\pi J}{\hbar} \), which reproduces the macroscopic Bekenstein-Hawking entropy \( S_{\text{macro}} = \frac{\text{Area}}{4\pi G} \). The results apply to any consistent unitary quantum theory of gravity with a Kerr solution, suggesting that extreme Kerr black holes are holographically dual to a chiral two-dimensional CFT. The authors conjecture that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with \( c_L \sim 2 \times 10^{79} \). The paper also discusses the asymptotic symmetry group, boundary conditions, and the computation of the central charge and temperature, providing a detailed analysis of the holographic duality in this context.The paper explores the holographic correspondence between quantum gravity near the horizon of an extreme Kerr black hole and a two-dimensional conformal field theory (CFT). The authors show that consistent boundary conditions exist, leading to the Virasoro algebra with a central charge \( c_L = \frac{12J}{\hbar} \). This implies that the near-horizon quantum states can be identified with those of a chiral half of a two-dimensional CFT. In the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with a dimensionless temperature \( T_L = \frac{1}{2\pi} \) and conjugate energy given by the zero mode generator \( L_0 \) of the Virasoro algebra. Assuming unitarity, the Cardy formula gives a microscopic entropy \( S_{\text{micro}} = \frac{2\pi J}{\hbar} \), which reproduces the macroscopic Bekenstein-Hawking entropy \( S_{\text{macro}} = \frac{\text{Area}}{4\pi G} \). The results apply to any consistent unitary quantum theory of gravity with a Kerr solution, suggesting that extreme Kerr black holes are holographically dual to a chiral two-dimensional CFT. The authors conjecture that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with \( c_L \sim 2 \times 10^{79} \). The paper also discusses the asymptotic symmetry group, boundary conditions, and the computation of the central charge and temperature, providing a detailed analysis of the holographic duality in this context.