Dynamics of Diffeomorphism Degrees of Freedom at a Horizon

Abstract

We define a set of boundary conditions that ensure the presence of a null hypersurface with the essential characteristics of a horizon, using the formalism of weakly isolated horizons as a guide. We then determine the diffeomorphisms that preserve these boundary conditions, and derive a dynamical action for these diffeomorphisms in a neighbourhood of the horizon. The action is similar to that of Liouville theory, and the equation of motion of the gravitational degrees of freedom approaches that of a free two-dimensional conformal field theory in the near-horizon region.

arXiv comment12 pages. Final version accepted for publication in Physical Review D

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• Noether Current, Horizon Virasoro Algebra and Entropy
• Noether current of the surface term of Einstein-Hilbert action, Virasoro algebra and entropy
• A Near Horizon CFT Dual for Kerr-Newman-$AdS$
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• Thermodynamics of nonspherical black holes from Liouville theory
• Near-Extremal Kerr AdS2xS2 Solution and Black-Hole/Near-Horizion-CFT Duality