带电压缩Kaluza-Klein黑洞度规的对称性分析
Symmetry analysis of the charged squashed Kaluza-Klein black hole metric
摘要：
本文讨论了黎曼空间中荷电压缩Kaluza-Klein黑洞时空的对称性和守恒律。首先，利用Lie点对称性对基本时空度量进行了全面的群分析，然后计算了该时空度量的$n$维最优系统，即$n=1,\ldots,4$.证明了不存在与$n\geq5$的测地线系统相联系的李对称子代数的$n$维最优系统。然后，求出了使拉格朗日量对应的作用积分保持不变的变换的单参数李群的点对称性（即Noether对称性），并利用Noether定理计算了测地线方程组的守恒律.
英文摘要：
In this paper, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza--Klein black hole spacetime in a Riemannian space is discussed. First, a comprehensive group analysis of the underlying space-time metric using Lie point symmetries are presented and then it the $n$-dimensional optimal system of this space-time metric, for $n=1,\ldots,4$, are computed. It is shown that there is not any $n$-dimensional optimal system of Lie symmetry subalgebra associated to the system of geodesic for $n\geq5$. Then the point symmetries of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian that means Noether symmetries are found and then the conservation laws associated to the system of geodesic equations are calculated via Noether's theorem.
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