Exact General Relativistic Rotating Disks Immersed in Rotating Dust Generated from van Stockum Solutions

Abstract

A class of exact general relativistic rotating thick disks surrounded by rotating dust is constructed by applying the ``displace, cut, fill and reflect'' method on the van Stockum class of metrics. Two particular solutions are considered in detail. We find that the disks have annular regions with negative energy density and heat flow is present in most of the radial extension of the disk. It is shown that thin disks are composed of exotic matter with an equation of state of cosmic strings or struts. We also comment the recent relativistic galactic model proposed by Cooperstock and Tieu and the presence of an additional disk of exotic matter in their model.