标题： 变分技巧在广义相对论中的应用：卡鲁扎理论的度量仿射方法 显示英文标题

标题： Variational techniques in general relativity: A metric-affine approach to Kaluza's theory

摘要： 一种新的广义相对论变分原理，基于一个涉及度规$\Phi\/$和联络$\nabla\/$作为独立自由度的泛函$I\/(\Phi,\nabla)\/$的作用量，提出了\emph{无约束}个自由度。 $I\/$的极值被看作是有序对$\/(\Phi,\nabla)\/$，其中$\Phi\/$是一个 Ricci 平坦度量，$\nabla\/$是相关的黎曼联络。 讨论了对 Kaluza 相互作用的引力和电磁场理论的应用。 显示英文摘要

摘要： A new variational principle for General Relativity, based on an action functional $I\/(\Phi,\nabla)\/$ involving both the metric $\Phi\/$ and the connection $\nabla\/$ as independent, \emph{unconstrained\/} degrees of freedom is presented. The extremals of $I\/$ are seen to be pairs $\/(\Phi,\nabla)\/$ in which $\Phi\/$ is a Ricci flat metric, and $\nabla\/$ is the associated Riemannian connection. An application to Kaluza's theory of interacting gravitational and electromagnetic fields is discussed.