On the ADM mass of critical area-normalized capacitors

TL;DR

This paper establishes mass-capacity inequalities for specific asymptotically flat manifolds, leading to new uniqueness results for Schwarzschild metrics and related spacetime configurations.

Contribution

It introduces mass-capacity inequalities for critical area-normalized capacitors and derives new uniqueness theorems for Schwarzschild and related spacetimes.

Findings

Proves mass-capacity inequalities for critical area-normalized capacitors.

Derives uniqueness results for Schwarzschild metrics.

Improves uniqueness theorems for certain asymptotically flat spacetimes.

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.