A Second Poincare' Group
A Second Poincare' Group
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发表时间：
1998-09
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通讯作者：
R. Aldrovandi;J. G. Pereira
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作者：
R. Aldrovandi;J. G. Pereira
利用德西特群和空间的 In\"on\u-Wigner 收缩讨论了具有弱和强宇宙学常数的无源爱因斯坦方程的解。更常见的情况对应于弱宇宙常数极限，其中德西特群收缩为庞加莱群，并且德西特空间缩减为闵可夫斯基空间。然而，在强宇宙常数极限下，德西特群收缩为另一个具有与庞加莱群相同的抽象李代数的群，并且德西特空间被简化为无限标量曲率的 4 维锥体空间，但黎曼和里奇曲率张量消失。在这样的空间中，特殊共角变换是传递性的，惯性系之间的等价性就是狭义相对论。
Solutions of the sourceless Einstein's equation with weak and strong cosmological constants are discussed by using In\"on\"u-Wigner contractions of the de Sitter groups and spaces. The more usual case corresponds to a weak cosmological-constant limit, in which the de Sitter groups are contracted to the Poincar\'e group, and the de Sitter spaces are reduced to the Minkowski space. In the strong cosmological-constant limit, however, the de Sitter groups are contracted to another group which has the same abstract Lie algebra of the Poincar\'e group, and the de Sitter spaces are reduced to a 4-dimensional cone-space of infinite scalar curvature, but vanishing Riemann and Ricci curvature tensors. In such space, the special conformal transformations act transitively, and the equivalence between inertial frames is that of special relativity.