Positive Energy Theorems for Spin Initial Data with Charge

Abstract

We establish positive energy theorems for complete spin initial data sets with charge in dimensions $n\ge 4$, under a dominant energy condition and assuming the existence of at least one asymptotically flat end. Our results, formulated in the purely electric case, extend the classical theorems of Gibbons--Hull~\cite{GibbonsHull}, Gibbons--Hawking--Horowitz--Perry~\cite{GibbonsHawkingHorowitzPerry}, and Bartnik--Chruściel~\cite{BartnikChrusciel}.