Magnetohydrodynamics, Dark Energy and Closed Null Curves: Towards a Family of Astrophysical Compact Objects

Abstract

Starting with a static, spherically symmetric spacetime incorporating critical (unstable) closed null geodesics, a family of models for equilibrium states of non-isolated compact objects is obtained by solving the Einstein equations for an energy-momentum tensor featuring a perfect fluid with ideal-gas equation of state, dark energy, and a magnetic field. All of these source fields are described by simple, monotonically decreasing mathematical functions. No ansatz is made for either of the two unknown metric elements;the null curve geometry yields one, and the other follows from a simplification of the magnetic field vector. The metric elements are free of singularities and horizons everywhere, although their inverses are singular at the origin. The entire metric assumes its Lorentzian form at infinity. The geometry of this model, as well as fundamental quantum considerations, require that the radial coordinate must always be greater than zero, thereby obviating the physical singularity at the origin.