Non- minimally Coupled Scalar Fields, Holst Action and Black Hole Mechanics

TL;DR

This paper extends the Weak Isolated Horizon framework to non-minimally coupled scalar fields within the Holst action, deriving black hole mechanics laws and linking horizon symplectic structure to a scalar-dependent U(1) Chern-Simons theory.

Contribution

It introduces a non-minimal scalar coupling in the Holst action, constructs the covariant phase space, and relates the horizon symplectic structure to a scalar-dependent Chern-Simons theory.

Findings

Proved laws of black hole mechanics in the non-minimal coupling context.

Derived the horizon symplectic structure as a U(1) Chern-Simons theory.

Showed the Chern-Simons level depends on the scalar field.

Abstract

The paper deals with the extension of the Weak Isolated Horizon (WIH) formulation to the non- minimally coupled Holst action. In the first part of the paper, we introduce the non- minimal scalar coupling of the Holst action and construct the covariant phase space of the theory. Using the covariant phase space, we prove the laws of black hole mechanics and show that with a gauge fixing, the symplectic structure on the horizon reduces to that of a U(1) Chern-Simons theory. The level of the Chern- Simons theory is shown to depend on the non-minimally coupled scalar field.