When null energy condition meets ADM mass

We give a conjecture on the lower bound of the ADM mass M by using the null energy condition. The conjecture includes a Penrose-like inequality 3M >= kA/(4 pi) + root A/4 pi and the Penrose inequality 2M >= root A/4 pi with A the event horizon area and n the surface gravity. Both the conjecture in the static spherically symmetric case and the Penrose inequality for a dynamical spacetime with spherical symmetry are proved by imposing the null energy condition. We then generalize the conjecture to a general dynamical spacetime. Our results raise a new challenge for the famous unsettled question in general relativity: in what general case can the null energy condition replace other energy conditions to ensure the Penrose inequality?

Automated summary

We propose a conjecture for the lower bound of ADM mass using the null energy condition. The conjecture is proved in specific scenarios and raises a new challenge for an unsettled question in general relativity.