标题： 诱导物质引力理论中的Gödel型时空 显示英文标题

标题： Gödel-type Spacetimes in Induced Matter Gravity Theory

摘要： 五维（5D）广义Gödel型流形在Cartan提出的等价问题方法的背景下被研究。 这些5D流形局部齐次的充要条件被推导出来。 这些齐次黎曼流形的局部等价性被探讨。 发现它们由三个本质参数$k$、$m^2$和$\omega$特征化：相同的三元组$(k, m^2, \omega)$对应于局部等价的5D流形。 一组不可约的等距非等价5D局部齐次黎曼广义Gödel型度规被展示。 基于本质参数对这些流形进行了分类，并确定了每类的Killing向量场及其对应的李代数。 结果显示，广义Gödel型五维流形具有最大等距群 $G_r$，具体取决于基本参数 $k$、$m^2$和 $\omega$，分别为 $r=7$、$r=9$或 $r=15$。 这些同质Gödel型流形中因果性破坏的情况也被研究。 结果表明，在六个不可约类中的三个类中可以违反因果性。 找到了诱导物质（IM）场方程的唯一广义Gödel型解。 还讨论了诱导物质形式的一般相对论是否能有效治疗这类因果异常问题，这与Romero、Tavakol和Zalaletdinov最近的一篇文章有关。 显示英文摘要

摘要： A five-dimensional (5D) generalized G\"odel-type manifolds are examined in the light of the equivalence problem techniques, as formulated by Cartan. The necessary and sufficient conditions for local homogeneity of these 5D manifolds are derived. The local equivalence of these homogeneous Riemannian manifolds is studied. It is found that they are characterized by three essential parameters $k$, $m^2$ and $\omega$: identical triads $(k, m^2, \omega)$ correspond to locally equivalent 5D manifolds. An irreducible set of isometrically nonequivalent 5D locally homogeneous Riemannian generalized G\"odel-type metrics are exhibited. A classification of these manifolds based on the essential parameters is presented, and the Killing vector fields as well as the corresponding Lie algebra of each class are determined. It is shown that the generalized G\"odel-type 5D manifolds admit maximal group of isometry $G_r$ with $r=7$, $r=9$ or $r=15$ depending on the essential parameters $k$, $m^2$ and $\omega$. The breakdown of causality in all these classes of homogeneous G\"odel-type manifolds are also examined. It is found that in three out of the six irreducible classes the causality can be violated. The unique generalized G\"odel-type solution of the induced matter (IM) field equations is found. The question as to whether the induced matter version of general relativity is an effective therapy for these type of causal anomalies of general relativity is also discussed in connection with a recent article by Romero, Tavakol and Zalaletdinov.