We study the invariance properties of five-dimensional metrics and their corresponding geodesic equations of motion. In this context a number of five-dimensional models of the Einstein–Gauss–Bonnet (EGB) theory leading to black holes, wormholes and spacetime horns arising in a variety of situations are discussed in the context of variational symmetries of which each vector field, via Noether’s theorem (NT), provides a nontrivial conservation law. In particular, it is shown that algebraic structure of isometries and the variational conservation laws of the five-dimensional Einstein–Bonnet metric extend consistently from the well-known Minkowski, de-Sitter and Schwarzschild four-dimensional spacetimes to the considered five-dimensional ones. In the equivalent five-dimensional case, the maximal algebra of kvs is fifteen with eight additional Noether symmetries. Also, whereas the constant curvature five-dimensional case leads to fifteen kvs and one additional Noether symmetry and seven plus one in the minimal case, a number of metrics of the EGB theory in five dimensions give rise to algebras isomorphic a seven-dimensional algebra of kvs and a single additional Noether symmetry.

中文翻译：

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测量更高维度的对称性和等距

我们研究了五维度量的不变性及其相应的测地线运动方程。在这种情况下，在变分对称的背景下讨论了爱因斯坦-高斯-博内 (EGB) 理论的许多五维模型，这些模型导致在各种情况下出现的黑洞、虫洞和时空角，其中每个向量场的变分对称性，通过诺特定理 (NT)，提供了一个非平凡的守恒定律。特别是，它表明等距的代数结构和五维 Einstein-Bonnet 度量的变分守恒定律从著名的 Minkowski、de-Sitter 和 Schwarzschild 四维时空一直延伸到所考虑的五维时空. 在等效的五维情况下，kvs 的最大代数是 15，另外还有 8 个 Noether 对称性。此外，虽然恒定曲率五维情况导致 15 kvs 和一个额外的 Noether 对称性以及在最小情况下的七加一，但 EGB 理论的许多五维度量导致代数同构的七维代数kvs 和一个额外的 Noether 对称性。