Research on the Group Structure of the Einstein Equations Solution Manifold

[307762]恩斯特博士将开展一个数学引力物理的研究项目。他将采用I. Hauser和他自己设计的技术来确定当任意指定的重力平面波碰撞时发生的时空扭曲，并确定当在旋转轴上任意指定引力势时与旋转质量相关的时空曲率。他还将研究将类似技术应用于不太理想的物理问题的可能性。当问题的复杂性要求采用数值计算和图形显示的方法时，将补充纯解析方法。利用广义相对论解决更现实的引力问题的尝试应该会继续产生新的数学技术，这些技术也可以应用于其他非线性物理理论，并且应该会对一般的非线性现象提供更深入的了解。＊＊＊

9307762 Ernst Dr. Ernst will carry out a program of research in mathematical gravitational physics. He will employ techniques devised by I. Hauser and himself to determine the spacetime distortion that takes place when arbitrarily specified gravitational plane waves collide, and to determine the spacetime curvature associated with spinning masses when the gravitational potential is specified arbitrarily on the axis of rotation. He will also study the possible application of similar techniques to physical problems that are less idealized. Purely analytical methods will be supplemented by numerical computation and graphical display whenever the complexity of the problem demands such an approach. The attempt to solve ever more realistic gravitational problems using the general theory of relativity should continue to spawn new mathematical techniques that can be applied as well to other nonlinear physical theories, and which should provide a deeper insight into nonlinear phenomena in general. ***