Godel Type Metrics in Randall Sundrum Model

TL;DR

This paper explores G"odel type metrics within the Randall-Sundrum brane-world framework, showing how extra dimension stabilization influences rotation parameters and the implications for cosmological models.

Contribution

It introduces G"odel type solutions in the Randall-Sundrum model and analyzes the stabilization of the extra dimension through the rotation parameter.

Findings

The rotation parameter is stabilized at about 10^{-32}.

The model effectively explains the lack of observable rotation in our universe.

A limiting case reproduces the Randall-Sundrum 2 model.

Abstract

Anisotropic cosmological models such as the G\"{o}del universe and its extensions - G\"{o}del type solutions, are embedded on a visible 3-brane in the Randall-Sundrum 1 model. The size of the extra dimension is stabilized by tuning the rotation parameter to a very small value so that hierarchy problem can be solved. A limiting case also yields the Randall-Sundrum 2 model. The rotation parameter on the visible brane turns out to be of order $10^{-32}$, which implies that visible brane essentially lacks rotation.