November 26, 2024 | Monica Guica, Thomas Hartman, Wei Song, and Andrew Strominger
The Kerr/CFT correspondence explores the relationship between extreme Kerr black holes and two-dimensional conformal field theories (CFTs). The paper shows that the near-horizon region of an extreme Kerr black hole, where angular momentum $ J $ equals $ GM^2 $, supports a consistent set of boundary conditions. These conditions lead to a Virasoro algebra with central charge $ c_L = \frac{12J}{\hbar} $, implying that the quantum states near the horizon correspond to those of a chiral CFT. In the extreme limit, the Frolov-Thorne vacuum state becomes a thermal density matrix with temperature $ T_L = \frac{1}{2\pi} $, and the Cardy formula applied to this CFT reproduces the Bekenstein-Hawking entropy $ S_{macro} = \frac{Area}{4\hbar G} $. The results suggest that extreme Kerr black holes are holographically dual to a chiral CFT with central charge $ c_L = \frac{12J}{\hbar} $. This duality applies to any consistent unitary quantum theory of gravity with a Kerr solution. The paper also discusses the implications for near-extreme black holes like GRS 1915+105, which is approximately dual to a CFT with $ c_L \sim 2 \times 10^{79} $. The analysis involves the near-horizon geometry of Kerr, the asymptotic symmetry group, boundary conditions, and the computation of central charge and temperature. The study confirms that the microscopic entropy of the CFT matches the macroscopic Bekenstein-Hawking entropy, supporting the holographic duality between extreme Kerr black holes and a chiral CFT.The Kerr/CFT correspondence explores the relationship between extreme Kerr black holes and two-dimensional conformal field theories (CFTs). The paper shows that the near-horizon region of an extreme Kerr black hole, where angular momentum $ J $ equals $ GM^2 $, supports a consistent set of boundary conditions. These conditions lead to a Virasoro algebra with central charge $ c_L = \frac{12J}{\hbar} $, implying that the quantum states near the horizon correspond to those of a chiral CFT. In the extreme limit, the Frolov-Thorne vacuum state becomes a thermal density matrix with temperature $ T_L = \frac{1}{2\pi} $, and the Cardy formula applied to this CFT reproduces the Bekenstein-Hawking entropy $ S_{macro} = \frac{Area}{4\hbar G} $. The results suggest that extreme Kerr black holes are holographically dual to a chiral CFT with central charge $ c_L = \frac{12J}{\hbar} $. This duality applies to any consistent unitary quantum theory of gravity with a Kerr solution. The paper also discusses the implications for near-extreme black holes like GRS 1915+105, which is approximately dual to a CFT with $ c_L \sim 2 \times 10^{79} $. The analysis involves the near-horizon geometry of Kerr, the asymptotic symmetry group, boundary conditions, and the computation of central charge and temperature. The study confirms that the microscopic entropy of the CFT matches the macroscopic Bekenstein-Hawking entropy, supporting the holographic duality between extreme Kerr black holes and a chiral CFT.