On shear-free motion of charged perfect fluid obeying an equation of state in general relativity (Q1821670)

The author investigates the general relativistic spherically symmetric charged perfect fluid scheme when the latter executes shear motion and it obeys an equation of state. The paper improves on a previous paper of \textit{B. Mashhoon} and \textit{M. H. Partovi} [Ann. Phys. 130, 99-138 (1980; Zbl 0456.76104)] in that it exhibits a new possible solution which is characterized by three parameters, one naturally being the charge parameter. This solution obtained through straightforward algebra by assuming a special form of the equation of state, has the property to go over to the Wyman metric for vanishing electric charge. However, with charge present it does not match with the Reissner-Nordström solution at a boundary and, therefore, does not qualify to represent a bounded system. Neither is it admissible to represent the dynamics of the universe. Clearly, imposing the validity of a classical pressure-density equation of state for spherically symmetric perfect fluid distributions executing shear-free motion severely restricts the class of admissible solutions. In the course of the discussion the author obtains certain regularity results which extend what is known for a neutral fluid to the case of a charged perfect fluid.