（2+1）维轴向宇宙--爱因斯坦方程的解、降维点和Klein-Fock-Gordon波
The (2+1)-dim Axial Universes -- Solutions to the Einstein Equations, Dimensional Reduction Points, and Klein-Fock-Gordon Waves
摘要：
本文给出了我们最近的出版物的推广和进一步的发展，其中Klein-Fock-Gordon方程的几个特定的$D=(2+1)$ -dim静态时空流形上定义的解决方案被认为是。后者涉及玩具模型的2维空间与轴对称，包括降维的1维空间作为一个奇异的限制情况。这里考虑的是具有轴对称的空间几何非静态模型。为了使这些模型更接近物理现实，我们定义了一组“可接受的”形函数$ρ(t,z)$作为$(2+1)$ -dim爱因斯坦方程的解在真空时空中，在存在$Λ$ -项，并为充满标准“灰尘”的时空。奇怪的是，在最后一种情况下，爱因斯坦方程简化为著名的蒙赫-安培方程，从而使人们能够获得柯西问题的通解，以及一组涉及一个任意函数的其他特定解。给出了Klein-Fock-Gordon方程在该集合中的几个显式解。这些解决方案的一个有趣的定性特征涉及到降维点，它们的分类和时间行为。特别是，这些新的实体可以为我们提供对P-和T-破坏以及大爆炸本质的新见解。一个简短的比较与其他尝试利用降维的时空。
英文摘要：
The paper presents a generalization and further development of our recent publications where solutions of the Klein-Fock-Gordon equation defined on a few particular $D=(2+1)$-dim static space-time manifolds were considered. The latter involve toy models of 2-dim spaces with axial symmetry, including dimension reduction to the 1-dim space as a singular limiting case. Here the non-static models of space geometry with axial symmetry are under consideration. To make these models closer to physical reality, we define a set of "admissible" shape functions $ρ(t,z)$ as the $(2+1)$-dim Einstein equations solutions in the vacuum space-time, in the presence of the $Λ$-term, and for the space-time filled with the standard "dust". It is curious that in the last case the Einstein equations reduce to the well-known Monge-Ampère equation, thus enabling one to obtain the general solution of the Cauchy problem, as well as a set of other specific solutions involving one arbitrary function. A few explicit solutions of the Klein-Fock-Gordon equation in this set are given. An interesting qualitative feature of these solutions relates to the dimension reduction points, their classification, and time behavior. In particular, these new entities could provide us with novel insight into the nature of P- and T-violation, and of Big Bang. A short comparison with other attempts to utilize dimensional reduction of the space-time is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
