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arXiv · 2205.08246

When null energy condition meets ADM mass

Run-Qiu Yang·Li Li·Rong-Gen Cai
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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?

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Run-Qiu Yang, Li Li, Rong-Gen Cai. 2022-05-17. When null energy condition meets ADM mass. https://doi.org/10.1088/1572-9494%2Fac84cd

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