Dynamics of Diffeomorphism Degrees of Freedom at a Horizon

TL;DR

This paper investigates the boundary conditions and diffeomorphism symmetries near a horizon, deriving a Liouville-like action and showing the gravitational degrees of freedom behave like a 2D conformal field theory.

Contribution

It introduces a new set of boundary conditions for horizons and derives a dynamical action resembling Liouville theory, linking horizon dynamics to 2D conformal field theories.

Findings

Derived boundary conditions for null hypersurfaces resembling horizons

Identified diffeomorphisms preserving these boundary conditions

Established a Liouville-like action for horizon degrees of freedom

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.