Some New Classes of Solutions of the Einstein-Maxwell Equations

Abstract

Finding new exact and numerical solutions of the Einstein-Maxwell eld equations (EMFEs) is one of the fundamental area of research. The exact solutions which satisfy the physical criteria of compact objects can be considered as models for the compact object like neutron stars, and dark energy objects. The exact form of the equation of state satis ed by the compact objects is unknown. In order to obtain new models for compact objects, one generally chooses some equation of state, for example, linear equation of state, quadratic equation of state, or some other form. We obtain a new model for the dark energy star with linear equation of state, pr = ð€€€ , where pr is the radial pressure and is the density. The physical criteria and stability of the model are investigated. A new solution with linear equation of state for ordinary matter object is obtained and the physical criteria and stability are discussed. By adding the initial conditions to the EFEs we get the Cauchy-Einstein eld equations (CEFEs). In literature many solutions have been obtained for the CEFEs. An extension is done by adding charge into CEFEs. The constraints and evolution equations for the Cauchy Einstein-Maxwell eld equations (CEMFEs) are given which can be solved for the cosmological universe which contains N discrete electrically charged black holes. For the simplicity, only regularly arranged charged masses in a 3-sphere are considered. The cosmological universe with N charged masses consists of linearly superposed Reissner-Nordstrom masses which represent the universe with discrete charged masses. In particular, a solution for 8-mass charged cosmological universe is obtained. These solutions generalize the Majumdar-Papapetrou solutions away from the extremal limit of charged black holes, and provide what we believe to be some of the rst relativistic calculations of the e ects of electric charge on cosmological backreaction.