# Asymptotically flat extensions with charge

## TL;DR

This paper extends techniques for constructing asymptotically flat initial data sets to include charge, enabling the computation of a charged version of the Bartnik mass for certain data.

## Contribution

It develops new extension and gluing tools for Einstein-Maxwell initial data, allowing calculation of a charged Bartnik mass for specific minimal data.

## Key findings

- Successfully constructed charged asymptotically flat extensions.
- Computed the charged Bartnik mass for certain minimal data.
- Extended Mantoulidis and Schoen's methods to include charge.

## Abstract

The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [2016] developed a novel technique to construct asymptotically flat extensions of minimal Bartnik data in such a way that the ADM mass of these extensions is well-controlled, and thus, they were able to compute the Bartnik mass for minimal spheres satisfying a stability condition. In this work, we develop extensions and gluing tools, \`a la Mantoulidis and Schoen, for time-symmetric initial data sets for the Einstein-Maxwell equations that allow us to compute the value of an ad-hoc notion of charged Barnik mass for suitable charged minimal Bartnik data.