Godel Type Metrics in Randall Sundrum Model

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.