Energy Conditions in Jordan Frame

TL;DR

This paper generalizes the null energy condition to the Jordan frame with non-minimal matter coupling, ensuring the second law of black hole thermodynamics holds in this frame.

Contribution

It introduces a new form of the null energy condition applicable to the Jordan frame, bridging the gap with Einstein frame formulations.

Findings

Generalized null energy condition for Jordan frame

Proof of black hole second law in Jordan frame

Consistency with Einstein frame results

Abstract

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.