The (2+1)-dim Axial Universes -- Solutions to the Einstein Equations, Dimensional Reduction Points, and Klein-Fock-Gordon Waves

Understand

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 $\rho(t,z)$ as the $(2+1)$-dim Einstein equations solutions in the vacuum space-time, in the presence of the $\Lambda$-term, and for the space-time filled with the standard "dust".