A generalized equation of motion for gravity theories with non-minimal   kinetic scalar couplings
  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. 
Saugata Chatterjee
gr-qc hep-th