The Kerr/CFT Correspondence

TL;DR

The paper proposes that extremal Kerr black holes are holographically dual to a chiral 2D CFT. By focusing on the near-horizon extreme Kerr geometry (NHEK) and imposing a specific set of boundary conditions, it identifies a single Virasoro algebra as the asymptotic symmetry with central charge $c_L=12J/\hbar$. Using the Frolov–Thorne vacuum to define a left-moving temperature $T_L=1/(2\pi)$ and applying the Cardy formula reproduces the Bekenstein–Hawking entropy $S_{BH}=2\pi J/\hbar$, providing microscopic support for Kerr/CFT. The framework is general to any consistent unitary quantum gravity theory containing the Kerr solution and suggests a holographic description for near-extremal black holes like GRS 1915+105. The work lays a foundation for understanding Kerr entropy through a 2D CFT and motivates further exploration of near-extremal excitations and boundary conditions.

Abstract

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}.