广义相对论是目前关于引力的标准理论，但理论和观测上的证据都提示广义相对论需要被修正。作为修改引力理论之一，Einstein-dilaton-Gauss-Bonnet（EdGB）理论是一个非常丰富而有趣的理论，它符合弱场验证，但在强场区域有可能观测到与广义相对论的明显区别。尤其是最近发现的EdGB理论黑洞自发标量化现象，更是掀起了研究该理论的热潮。然而这些研究多局限于静态或线性微扰情况，关于该理论的非线性动力学鲜有研究，是亟待深入挖掘的研究方向。本项目将聚焦EdGB理论中的非线性行为，包括利用数值方法模拟该理论的引力坍缩、黑洞自发标量化的动力学演化等，研究电荷、宇宙学常数、高阶曲率项对动力学的影响。我们还将从数值与解析角度分析EdGB理论运动方程的适定性。这些研究不仅会加深我们对引力本质的认识，研究过程中发展起来的数值方法，未来还可以用于研究双黑洞并合的引力波。

General relativity is the current standard theory for gravity. But the evidences from both theory and observation imply that it should be modified. As one of the modified gravity, the Einstein-dilaton-Gauss-Bonnet (EdGB）theory is a rich and interesting theory. It matches the test from weak field, and also show significant deviations from general relativity in strong field regime. Especially, the enthusiasm for EdGB theory was inspired by the recent discovery of the black hole spontaneous scalarization in EdGB theory. However, these studies were limited in static or linear perturbation cases. The nonlinear dynamics in EdGB theory should be studied urgently but seldom was done for now. This project will focus on the nonlinear behaviors in EdGB theory, including the gravitational collapse and dynamics of the black hole spontaneous scalarization. We will study the effects of the charge, cosmological constant and higher order curvature term on the dynamics numerically. We will also study the well-posedness of equations of motion of EdGB theory both numerically and analytically. These studies will deepen our understanding of the nature of gravity. The numerical method developed in this project will be used to study the binary black hole merger and gravitational wave in the future.