When null energy condition meets ADM mass

TL;DR

This paper proposes a new conjecture linking the null energy condition to lower bounds on ADM mass, proves related inequalities in symmetric cases, and explores their generalization to dynamical spacetimes, challenging existing assumptions in general relativity.

Contribution

It introduces a novel conjecture connecting null energy condition with ADM mass bounds and proves related inequalities in symmetric cases, extending to dynamical spacetimes.

Findings

Proved Penrose-like inequality in static spherically symmetric case

Established Penrose inequality for dynamical spherically symmetric spacetime

Proposed a generalized conjecture for dynamical spacetimes

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 $3M\geq\kappa\mathcal{A}/(4\pi)+\sqrt{\mathcal{A}/4\pi}$ and the Penrose inequality $ 2M\geq\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?