Classical solutions in five dimensional induced matter theory and its relation to an imperfect fluid

TL;DR

This paper explores five-dimensional cosmological models with Bianchi type I and V hypersurfaces, showing that the induced four-dimensional matter behaves as an imperfect fluid with dissipative properties, derived purely from geometry.

Contribution

It demonstrates how vacuum solutions in five dimensions induce a four-dimensional imperfect fluid, linking higher-dimensional geometry to observable matter properties.

Findings

Induced matter has an imperfect fluid structure.

Dissipative terms naturally arise from the fifth dimension.

Models include Bianchi type I and V cosmologies.

Abstract

We study five dimensional cosmological models with four dimensional hypersufaces of the Bianchi type I and V. In this way the five dimensional vacuum field equations $\rm G_{AB} = 0$, led us to four dimensional matter equations $\rm G_{\mu\nu}=T_{\mu\nu}$ and the matter is interpreted as a purely geometrical property of a fifth dimension. Also, we find that the energy-momentum tensor induced from the fifth dimension has the structure of an imperfect fluid that has dissipative terms.