  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.
