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<p>In this note, we establish mass–capacity inequalities for asymptotically flat manifolds whose boundary capacity potential satisfies an overdetermined boundary condition—so-called critical area-normalized capacitors. As a consequence, we derive uniqueness results for the Schwarzschild metric and sharpen uniqueness theorems for spin asymptotically flat static vacuum spacetimes with a connected photon surface, as well as for spin asymptotically flat static manifolds satisfying an overdetermined Robin-type boundary condition.</p>

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On the ADM mass of critical area-normalized capacitors

  • 期刊论文

  • 发表日期：

    2025年12月15日

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  • Simon Raulot

摘要

In this note, we establish mass–capacity inequalities for asymptotically flat manifolds whose boundary capacity potential satisfies an overdetermined boundary condition—so-called critical area-normalized capacitors. As a consequence, we derive uniqueness results for the Schwarzschild metric and sharpen uniqueness theorems for spin asymptotically flat static vacuum spacetimes with a connected photon surface, as well as for spin asymptotically flat static manifolds satisfying an overdetermined Robin-type boundary condition.