The entropy of isolated horizons in non-minimally coupling scalar field theory from BF theory

TL;DR

This paper calculates the entropy of isolated horizons in non-minimally coupled scalar field and scalar-tensor gravitation theories using boundary BF theory in loop quantum gravity, matching the Wald entropy without symmetry constraints.

Contribution

It introduces a boundary BF theory approach for entropy calculation, avoiding the need for spherical symmetry and aligning with Wald entropy results.

Findings

Boundary BF theory effectively reproduces Wald entropy.

No spherical symmetry assumption is required.

Results match classical Wald entropy formula.

Abstract

In this paper, the entropy of isolated horizons in non-minimally coupling scalar field theory and in the scalar-tensor theory of gravitation is calculated by counting the degree of freedom of quantum states in loop quantum gravity. Instead of boundary Chern-Simons theory, the boundary BF theory is used. The advantages of the new approaches are that no spherical symmetry is needed, and that the final result matches exactly with the Wald entropy formula.