黑洞的稳定性与Cosmic Censorship假设一直是推进数学广义相对论发展的重要动力与研究热点。本项目围绕这两个世界性前沿问题，提出Einstein Yang-Mills模型(EYM)。在球对称假设下，EYM仍具有动力学行为，既方便数学上的探索又有客观物理意义。本项目以物理中数值实验为基础，探索球对称EYM下黑洞的形成机制与稳定性。Reissner-Nordström黑洞和Schwarzschild黑洞解均是EYM的特殊球对称解。我们提出不同的初值条件，分别探测两类黑洞的形成，并证明EYM在黑洞外部的整体存在性。进一步，我们考虑Schwarzschild黑洞在该系统下的稳定性，并且构造Morawetz估计获得衰减速度。此外，我们将研究最终形成的Schwarzschild黑洞质量与初始黑洞质量之间的关系。通过本项目的探索，将促进对黑洞形成与稳定等经典难题的解决。

The stability of black holes and the cosmic censorship conjecture have been promoting the development of Mathematical General Relativity and intensively studied. With respect to this trend, we present the Einstein Yang-Mills model(EYM). With spherical symmetry, EYM is still dynamical, which would be favorable for mathematical study and it is also a physical model. Based on the numerical study in physics, we will investigate the formation of black holes and nonlinear stability for EYM. Reissner-Nordström and Schwarzschild black holes are both spherical symmetric solutions of EYM. We will present different initial data, detect the formation of these two black holes separately and prove the global existence of EYM in the exterior. Furthermore, we will prove that under spherical symmetric perturbation, the spacetime will finally decay to Schwarzschild black hole. Moreover, we will make use of the Morawetz estimate to calculate the decay rate. Besides, the relation between the final Bondi mass and initial Bondi mass will also be investigated. This project will contribute a lot to understand the puzzle about formation and stability of black holes.