The Kerr/CFT Correspondence (0809.4266v1)

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=1/2\pi and 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}=2\pi J / \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}.

• The paper establishes that extreme Kerr black holes are dual to a chiral 2D CFT by deriving boundary conditions that yield a Virasoro algebra with a central charge.
• It employs the Cardy formula to relate the central charge to the microscopic entropy, matching the macroscopic Bekenstein-Hawking entropy.
• The study broadens holographic duality beyond the AdS/CFT framework, paving the way for further exploration in quantum gravity and non-extremal black holes.

An Expert Analysis of "The Kerr/CFT Correspondence"

The paper under review presents a significant exploration into the Kerr/CFT Correspondence, where the authors propose that extreme Kerr black holes are dual to a chiral two-dimensional conformal field theory (CFT) with a central charge $c_L = 12J/\hbar$. This conjecture extends the framework of holographic dualities beyond the classical AdS/CFT paradigm, suggesting a deep connection between the geometry near the horizon of extreme Kerr black holes and the rich structure of CFTs.

Summary of Core Contributions

The key breakthrough of this paper lies in establishing boundary conditions for the near-horizon extreme Kerr (NHEK) geometry, which yield an asymptotic symmetry group (ASG) characterized by the Virasoro algebra with a calculable central charge. The paper builds on the earlier work of Brown and Henneaux, offering a detailed derivation of the central charge, calculated to be $c_L = 12J/\hbar$ for a consistent unitarity-preserving quantum theory of gravity.

Central to their argument, the authors employ the Cardy formula to relate this Virasoro algebra's central charge to the microscopic entropy of the dual CFT, finding concordance with the macroscopic Bekenstein-Hawking entropy. This analysis provides compelling evidence for the duality by demonstrating that extreme Kerr black holes' microstates can accurately reproduce their macroscopic thermodynamic properties.

Theoretical Implications

The theoretical implications of this paper are layered and significant. Firstly, the reinterpretation of near-horizon Kerr black holes in terms of a dual CFT expands the potential applicability of holography to systems not constrained by the specificities of AdS spacetime. This development is pivotal in understanding the entropy of astrophysical black holes without reverting to string theory's microscopic descriptions.

Moreover, by articulating a framework that potentially extends beyond four-dimensional settings and to near-extreme black holes, this research enables broader explorations of black hole microstates through the lens of CFT. Such progress is anticipated to inspire further investigations into other astrophysical phenomena, including ISCO emissions, and foster new interpretations within high-energy and gravitational physics.

Strong Numerical and Conceptual Findings

The paper’s strong numerical results include the derivation of the central charge and the precise agreement of the Cardy formula with Bekenstein-Hawking entropy. Notably, with measurements like those for the black hole GRS 1915+105, where $J/GM > 0.98$, the experimental context complements the theoretical framework, suggesting the need for slight corrections in the dual CFT representation, hinting at general applicability to observable black holes.

Future Directions

The speculated future advancements stemming from this investigation are numerous. Notably, the prospects of examining non-chiral CFTs for near-extremal Kerr black holes promise further insights into black hole thermodynamics and quantum gravity. Additionally, understanding the subtleties of different boundary conditions and their implications for both extremal and non-extremal black holes remains an area ripe for exploration.

Conclusion

In sum, the paper "The Kerr/CFT Correspondence" augments our conceptual toolbox with a refined perspective on black hole physics, articulating a compelling duality with foundational implications for gravitational and high-energy theoretical physics. By situating extreme Kerr black holes within a conformal field theory framework, it lays the groundwork for novel inquiries into the intertwining fabric of spacetime geometry and quantum mechanics.