Vacuum initial data with minimal decay and borderline decay

TL;DR

This paper demonstrates that the Mao-Tao conical solution-operator method can construct vacuum asymptotically flat initial data at minimal and borderline decay thresholds, supporting stability results of Minkowski spacetime.

Contribution

It extends the Mao-Tao method to minimal and borderline decay initial data, linking to stability proofs of Minkowski spacetime.

Findings

Applicable to minimal and borderline decay initial data

Supports stability of Minkowski spacetime

Provides a new construction method for vacuum initial data

Abstract

In this note, we show that the conical solution-operator method of Mao-Tao in [Localized initial data for Einstein equations] applies to a simple construction of vacuum asymptotically flat initial data at minimal and borderline decay thresholds, corresponding to the global and exterior stability of Minkowski spacetime proved by the first named author in [Global stability of Minkowski spacetime with minimal decay] and [Exterior stability of Minkowski spacetime with borderline decay].