New asymptotically flat static vacuum metrics with near Euclidean boundary data

TL;DR

This paper advances the understanding of static vacuum metrics by identifying broad classes of boundary hypersurfaces that are static regular, supporting the construction of asymptotically flat solutions with near Euclidean boundary data.

Contribution

It improves previous results by showing that a large open and dense family of hypersurfaces are static regular, extending the class of boundary data for which static vacuum metrics can be constructed.

Findings

Large open and dense family of hypersurfaces are static regular

Static regularity holds under broader boundary conditions

Supports existence of asymptotically flat static vacuum metrics

Abstract

In our prior work toward Bartnik's static vacuum extension conjecture for near Euclidean boundary data, we establish a sufficient condition, called static regular, and confirm large classes of boundary hypersurfaces are static regular. In this note, we further improve some of those prior results. Specifically, we show that any hypersurface in an open and dense subfamily of a certain general smooth one-sided family of hypersurfaces (not necessarily a foliation) is static regular. The proof uses some of our new arguments motivated from studying the conjecture for boundary data near an arbitrary static vacuum metric.