Geometrostatic Manifolds of Small ADM Mass

TL;DR

This paper investigates the geometry of small-mass black hole configurations, establishing bounds on minimal surfaces and demonstrating stability of the positive mass theorem in these scenarios.

Contribution

It provides new bounds on minimal surfaces and proves intrinsic flat stability of the positive mass theorem for geometrostatic manifolds with small ADM mass.

Findings

Boundaries of outermost minimal surfaces are characterized.

Intrinsic flat stability of the positive mass theorem is established.

Results apply to configurations with small ADM mass relative to black hole separation.

Abstract

We bound the locations of outermost minimal surfaces in geometrostatic manifolds whose ADM mass is small relative to the separation between the black holes and prove the Intrinsic Flat Stability of the Positive Mass Theorem in this setting.