Off-shell Noether current and conserved charge in Horndeski theory

TL;DR

This paper develops a method to derive off-shell Noether currents and conserved charges in Horndeski theory, enabling analysis of black hole solutions with non-minimal scalar couplings.

Contribution

It introduces a novel off-shell Noether current and potential formulation for Horndeski theory, facilitating conserved charge calculations in complex scalar-tensor models.

Findings

Derived explicit off-shell Noether current and potential.

Calculated conserved charges for black holes in scalar-tensor theories.

Demonstrated applicability to non-minimally coupled scalar fields.

Abstract

We derive the off-shell Noether current and potential in the context of Horndeski theory, which is the most general scalar-tensor theory with a Lagrangian containing derivatives up to second order while yielding at most to second-order equations of motion in four dimensions. Then the formulation of conserved charges is proposed on basis of the off-shell Noether potential and the surface term got from the variation of the Lagrangian. As an application, we calculate the conserved charges of black holes in a scalar-tensor theory with non-minimal coupling between derivatives of the scalar field and the Einstein tensor.