Mechanics of Isolated Horizons in Scalar-Tensor Theories

TL;DR

This paper derives the symplectic form and first law of thermodynamics for isolated horizons in scalar-tensor theories, revealing the roles of the Immirzi parameter and scalar field in horizon properties.

Contribution

It introduces a covariant phase space approach to analyze isolated horizons in scalar-tensor theories, highlighting the effects of the Immirzi parameter and scalar field on horizon thermodynamics.

Findings

Immirzi parameter influences the angular momentum of the horizon.

Scalar field contributes to the horizon entropy.

First law of thermodynamics is established for weakly isolated horizons.

Abstract

Based on the first-order action for scalar-tensor theories with the Immirzi parameter, the symplectic form for the spacetimes admitting a weakly isolated horizon as internal boundary is derived by the covariant phase space approach. The first law of thermodynamics for the weakly isolated horizons with rotational symmetry is obtained. It turns out that the Immirzi parameter appears in the expression of the angular momentum of isolated horizon, and the scalar field contributes to the horizon entropy.