Petrov和Kaigorodov-Ozsváth解：作为群流形的时空
The Petrov and Kaigorodov-Ozsváth Solutions: Spacetime as a Group Manifold
摘要：
彼得罗夫解（对于$Λ=0$）和凯戈罗多夫-奥兹瓦思解（对于$Λ<0$）提供了具有简单传递等距群的爱因斯坦方程的真空解的例子。我们计算的边界应力张量Kaigorodov-Ozsváth解决方案的adS/CFT对应的上下文中。通过给出彼得罗夫解的Killing代数的矩阵表示，我们确定了群上的左不变1-形式。代数示出承认一个双参数家庭的线性变形的特殊情况下，给出了代数的Kaigorodov-Ozsváth解决方案。通过对这两种代数应用非线性实现的方法，我们从这两种情况下的一般一阶作用量得到了Finsler型拉格朗日量。解释彼得罗夫解决方案的外部解决方案的刚性旋转尘埃圆柱体，我们讨论的问题，创建CTC通过旋转这样的圆柱体。我们表明测地线完整的彼得罗夫和Kaigorodov Ozsváth解决方案，并确定在这些时空的测地线的行为。在这两种情况下，完整群都是由洛伦兹群给出的。
英文摘要：
The Petrov solution (for $Λ=0$) and the Kaigorodov-Ozsváth solution (for $Λ<0$) provide examples of vacuum solutions of the Einstein equations with simply-transitive isometry groups. We calculate the boundary stress-tensor for the Kaigorodov-Ozsváth solution in the context of the adS/CFT correspondence. By giving a matrix representation of the Killing algebra of the Petrov solution, we determine left-invariant one-forms on the group. The algebra is shown to admit a two-parameter family of linear deformations a special case of which gives the algebra of the Kaigorodov-Ozsváth solution. By applying the method of non-linear realisations to both algebras, we obtain a Lagrangian of Finsler type from the general first-order action in both cases. Interpreting the Petrov solution as the exterior solution of a rigidly rotating dust cylinder, we discuss the question of creation of CTCs by spinning up such a cylinder. We show geodesic completeness of the Petrov and Kaigorodov-Ozsváth solutions and determine the behaviour of geodesics in these spacetimes. The holonomy groups were shown to be given by the Lorentz group in both cases.
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