Exact Solutions of Five Dimensional Anisotropic Cosmologies

TL;DR

This paper derives exact solutions to five-dimensional vacuum Einstein equations for anisotropic cosmologies with Bianchi-II and V geometries, analyzing their behavior and implications for dimensional reduction within a Kaluza-Klein framework.

Contribution

It provides new exact solutions for five-dimensional anisotropic cosmologies with time and extra coordinate dependence, linking geometric properties to matter content.

Findings

Solutions exhibit contraction of the fifth dimension under certain parameters.

Dimensional reduction occurs naturally in these models.

Extra geometric terms can be interpreted as matter contributions in four dimensions.

Abstract

We solve the five dimensional vacuum Einstein equations for several kinds of anisotropic geometries. We consider metrics in which the spatial slices are characterized as Bianchi types-II and V, and the scale factors are dependent both on time and a non-compact fifth coordinate. We examine the behavior of the solutions we find, noting for which parameters they exhibit contraction over time of the fifth scale factor, leading naturally to dimensional reduction. We explore these within the context of the induced matter model: a Kaluza-Klein approach that associates the extra geometric terms due to the fifth coordinate with contributions to the four dimensional stress-energy tensor.