English

On the ADM mass of critical area-normalized capacitors

Differential Geometry 2025-01-24 v1

Abstract

In this note, we prove mass-capacity inequalities for asymptotically flat manifolds whose boundary capacity potential satisfies an overdetermined problem, referred to as critical area-normalized capacitors. As a consequence, we obtain uniqueness results for the Schwarzschild metric, from which improvements in the uniqueness theorems for spin asymptotically flat spacetimes containing a connected photon surface, as well as for spin asymptotically flat static manifolds with boundary are obtained.

Keywords

Cite

@article{arxiv.2501.13427,
  title  = {On the ADM mass of critical area-normalized capacitors},
  author = {Simon Raulot},
  journal= {arXiv preprint arXiv:2501.13427},
  year   = {2025}
}