Energy Conditions in Jordan Frame
  The null energy condition, in its usual form, can appear to be violated by transformations in the conformal frame of the metric. We propose a generalization of the form of the null energy condition to Jordan frame, in which matter is non-minimally coupled, which reduces to the familiar form in Einstein frame. Using our version of the null energy condition, we provide a direct proof of the second law of black hole thermodynamics in Jordan frame. 
Saugata Chatterjee, Damien A. Easson, and Maulik Parikh
gr-qc hep-th