In this paper we study the global existence and completeness of classical solutions of gravity coupled a scalar field system called Einstein–Klein–Gordon system in higher dimensions. We introduce a new ansatz function to reduce the problem into a single first-order integro-differential equation. Then, we employ the contraction mapping in the appropriate Banach space. Using Banach fixed theorem, we show that there exists a unique fixed point, which is the solution of the theory. For a given initial data, we prove the existence of both local and global classical solutions. We also study the completeness properties of the spacetime. Here, we introduce a mass-like function for \(D\ge 4\) in Bondi coordinates. The completeness of spacetime along the future directed timelike lines outward to a region which resembles the event horizon of the black hole.

在本文中，我们研究了高维中与称为爱因斯坦-克莱因-戈登系统的标量场系统耦合的重力经典解的全局存在性和完整性。我们引入一个新的 ansatz 函数将问题简化为单个一阶积分微分方程。然后，我们在适当的 Banach 空间中采用收缩映射。利用Banach不动定理，我们证明存在唯一的不动点，这就是该理论的解。对于给定的初始数据，我们证明局部和全局经典解的存在。我们还研究时空的完整性特性。在这里，我们引入了Bondi 坐标系中\(D\ge 4\)的类质量函数。未来时空的完整性将类时线向外引导到类似于黑洞事件视界的区域。