When null energy condition meets ADM mass

Abstract

Abstract 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 3 M ≥ κ  / ( 4 π ) +  / 4 π and the Penrose inequality 2 M ≥  / 4 π with  the event horizon area and κ 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?