Asymptotically flat extensions with 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, Ã 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.

We performed minor corrections in the statement of the main theorem related to the bound on the first eigenvalue, see Corollary 5.1 and Theorem 5.1. Moreover, we added remark on page 3 concerning the time-evolution of the initial data sets we construct. Comments are very welcome