Positive Energy Theorems for Spin Initial Data with Charge

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}.