Energy conditions in the 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 the Jordan frame, in which matter is non-minimally coupled, which reduces to the familiar form in the Einstein frame. Using our version of the null energy condition, we provide a direct proof of the second law of black hole thermodynamics in the Jordan frame.