Riemannian $(1+\mathbf{d})$-Dim Space-Time Manifolds with Nonstandard Topology which Admit Dimensional Reduction to Any Lower Dimension and Transformation of the Klein-Gordon Equation to the $1$-Dim Schrödinger Like Equation

Abstract

This rather technical paper presents some generalization of the results of recent publications \cite{Shirkov2010, DVPF2010, PFDV2010} where toy models of dimensional reduction of space-time were considered. Here we introduce and consider a specific type of multidimensional space-times with nontrivial topology and nontrivial Riemannian metric, which admit a reduction of the dimension $d$ of the space to any lower one $d_{low}=1,2,...,d-1$. The variable geometry is described by several variable radii of compactification of part of space dimensions. We succeed once more in transforming the shape of the variable geometry of the $d$-dimensional spaces under consideration to a specific potential interaction, described by the potential $V$ in the one-dimensional Schrödinger-like equation. This way one may hope to study the possible physical signals going from both higher and lower dimensions into our obviously four dimensional real world.

latex file, 5 pages, 1 figure

References in corpus (3)

• Spin dynamics in gravitational fields of rotating bodies and the equivalence principle
• Solution of the problem of uniqueness and hermiticity of hamiltonians for Dirac particles in gravitational fields
• Coupling running through the Looking-Glass of dimensional Reduction

Cited by in corpus (1)

• An Exploration of the Singularities in General Relativity