Induced Matter Theory of gravity from a Weitzenb\"ock 5D vacuum and pre-big bang collapse of the universe

TL;DR

This paper extends the Induced Matter Theory of gravity to 5D curved spacetimes using Weitzenb"ock representation, enabling new applications including modeling a pre-big bang universe collapse.

Contribution

It introduces a novel extension of IMT to 5D curved spacetimes via Weitzenb"ock representation, linking 5D geometry to 4D Einstein equations.

Findings

Weitzenb"ock representation simplifies 5D curvature tensor to null.

A static foliation induces 4D Einstein equations from 5D geometry.

Application to pre-big bang collapse scenario demonstrates the theory's potential.

Abstract

We extend the Induced Matter Theory of gravity (IMT) to 5D curved spacetimes by using the Weitzenb\"ock representation of connections on a 5D curved spacetime. In this representation the 5D curvature tensor becomes null, so that we can make a static foliation on the extra noncompact coordinate to induce in the Weitzenb\"ock representation the Einstein equations. Once we have done it, we can rewrite the effective 4D Einstein equations in the Levi-Civita representation. This generalization of IMT opens a huge window of possible applications for this theory. A pre-big bang collapsing scenario is explored as an example.