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# Advances in Theoretical and Mathematical Physics

## Volume 23 (2019)

### Number 8

### Asymptotically flat extensions with charge

Pages: 1951 – 1980

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n8.a1

#### Authors

#### Abstract

The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. Mantoulidis and Schoen [14] 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, *à la* Mantoulidis–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.