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In this paper we study the global existence and completeness of classicalsolutions of gravity coupled a scalar field system called Einstein-Klein-Gordonsystem in higher dimensions. We introduce a new ansatz function to reduce theproblem into a single first-order integro-differential equation. Then, weemploy the contraction mapping in the appropriate Banach space. Using Banachfixed theorem, we show that there exists a unique fixed point, which is thesolution of the theory. For a given initial data, we prove the existence ofboth local and global classical solutions. We also study the completenessproperties of the spacetime. Here, we introduce a mass-like function for $D\geq4$ in Bondi coordinates. The completeness of spacetime along the futuredirected timelike lines outward to a region which resembles the event horizonof the black hole.

Global Existence and Completeness of Classical Solutions in Higher Dimensional Einstein-Klein-Gordon System