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}
}