Systematic evaluation of quantum energy inequalities over observers

Develop a systematic procedure for evaluating quantum energy inequalities across all admissible observers at a spacetime point in general relativity, so that the inequalities can be verified over the full timelike (and, when applicable, null) observer manifold rather than for a single preferred frame.

Background

The paper presents a toolkit that verifies classical energy conditions (NEC, WEC, SEC, DEC) in an observer-robust manner by combining Hawking–Ellis algebraic classification with gradient-based optimization over the timelike and null observer manifolds.

While classical energy conditions are the focus, the authors note that quantum energy inequalities (QEIs) are often regarded as more physically realistic constraints on stress-energy. However, unlike the classical case addressed by their toolkit, the authors state that a systematic evaluation of QEIs over observers has not been established, identifying this as an open problem.