Static isolated horizons: SU(2) invariant phase space, quantization, and black hole entropy

TL;DR

This paper develops a SU(2) invariant formulation of static isolated horizons, proposes a quantization method for horizon degrees of freedom, and demonstrates consistency with black hole entropy without fixing the Immirzi parameter.

Contribution

It introduces a revised classical description for static isolated horizons and a novel quantization approach that aligns with the Hawking area law.

Findings

Agreement with Hawking's area law without fixing the Immirzi parameter

Restoration of diffeomorphism invariance by enlarging field content

Effective boundary theories for horizon degrees of freedom

Abstract

We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2) invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to the non conservation of the usual pre-symplectic structure. We argue how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism invariance. Restricting our attention to static isolated horizons we study the effective theories describing the boundary degrees of freedom. A quantization of the horizon degrees of freedom is proposed. By defining a statistical mechanical ensemble where only the area A of the horizon is fixed macroscopically-states with fluctuations away from spherical symmetry are allowed-we show that it is possible to obtain agreement with the Hawking's area law---S = A/4 (in Planck Units)---without fixing the Immirzi parameter to any particular value: consistency with the area law only imposes a relationship between the Immirzi parameter and the level of the Chern-Simons theory involved in the effective description of the horizon degrees of freedom.