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 = ,
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.
