Reformulation of Boundary BF Theory Approach to Statistical Explanation of the Entropy of Isolated Horizons

TL;DR

This paper demonstrates that the symplectic form for a system combining bulk Palatini gravity and boundary SO(1,1) BF theory simplifies to a bulk term, offering a new perspective on the entropy of isolated horizons.

Contribution

It introduces an alternative quantization method for boundary BF theory and links horizon entropy to bulk spin network states satisfying specific boundary conditions.

Findings

Symplectic form contains only bulk term for the combined system.

Boundary BF theory can be quantized using a new approach.

Horizon entropy relates to bulk spin network degrees of freedom.

Abstract

It is shown in this paper that the symplectic form for the system consisting of $D$-dimensional bulk Palatini gravity and SO$(1,1)$ BF theory on an isolated horizon as a boundary just contains the bulk term. An alternative quantization procedure for the boundary BF theory is presented. The area entropy is determined by the degree of freedom of the bulk spin network states which satisfy a suitable boundary condition. The gauge-fixing condition in the approach and the advantages of the approach are also discussed.