Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 8

Asymptotically flat extensions with charge

Pages: 1951 – 1980



Aghil Alaee (Center of Mathematical Sciences and Applications, Harvard University, Cambridge Massachusetts, U.S.A.)

Armando J. Cabrera Pacheco (Department of Mathematics, Universität Tübingen, Germany)

Carla Cederbaum (Department of Mathematics, Universität Tübingen, Germany)


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.