When null energy condition meets ADM mass

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 $3M\ge \kappa \mathcal{A}/(4\pi )+\sqrt{\mathcal{A}/4\pi }$ and the Penrose inequality $2M\ge \sqrt{\mathcal{A}/4\pi }$ with $\mathcal{A}$ the event horizon area and $\kappa$ 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?

7 pages, no figure

References in corpus (4)

• Present status of the Penrose inequality
• The Penrose inequality and apparent horizons
• A poor man's positive energy theorem: II. Null geodesics
• From bending of light to positive mass: a non-PDE perspective