A generalized equation of motion for gravity theories with non-minimal kinetic scalar couplings

TL;DR

This paper derives a generalized equation of motion for higher-curvature gravity theories that include non-minimal kinetic scalar couplings, addressing subtle features absent in Einstein-Hilbert gravity.

Contribution

It provides a unified framework and an algorithmic method to derive equations of motion for complex gravity theories with non-minimal scalar couplings.

Findings

Derived a general form of the equation of motion for such theories

Identified subtle features unique to higher-curvature gravity

Presented an algorithmic prescription for evaluation

Abstract

A general form for the equation of motion for higher-curvature gravity is obtained. The interesting feature of the analysis is that it can handle Lagrangians which contain non-minimal kinetic scalar couplings. Certain subtle features, which are absent for the Einstein-Hilbert term, arise in higher-curvature gravity. These are identified and an algorithmic prescription is presented for the evaluation of the generalized equation of motion.