Study of charged compact stars with class 1 metric under general relativity

In the present paper we study compact stars under the background of Einstein–Maxwell space–time, where the 4-dimensional spherically symmetric space–time of class 1 along with the Karmarkar condition has been adopted. The investigations, via the set of exact solutions, show several important results, such as (i) the value of density on the surface is finite; (ii) due to the presence of the electric field, the outer surface or the crust region can be considered to be made of electron cloud; (iii) the charge increases rapidly after crossing a certain cutoff region (r/R ≈ 0.3); and (iv) the avalanche of charge has a possible interaction with the particles that are away from the center. As the stellar structure supports all the physical tests performed on it, therefore the overall observation is that the model provides a physically viable and stable compact star.

PHYSICAL PROPERTIES OF TOLMAN–BAYIN SOLUTIONS: SOME CASES OF STATIC CHARGED FLUID SPHERES IN GENERAL RELATIVITY

In this article, Einstein–Maxwell space–time is considered in connection with some of the astrophysical solutions previously obtained by Tolman (1939) and Bayin (1978). The effect of inclusion of charge in these solutions is investigated thoroughly and the nature of fluid pressure and mass density throughout the sphere is discussed. Mass–radius and mass–charge relations are derived for various cases of the charged matter distribution. Two cases are obtained where perfect fluid with positive pressures gives rise to electromagnetic mass models such that gravitational mass is of purely electromagnetic origin.

The Einstein pseudo-tensor and the flux integral for perturbed static space-times

The flux integral for axisymmetric polar perturbations of static vacuum space-times, derived in an earlier paper directly from the relevant linearized Einstein equations, is rederived with the aid of the Einstein pseudo-tensor by a simple algorism. A similar earlier effort with the aid of the Landau–Lifshitz pseudo-tensor failed. The success with the Einstein pseudo-tensor is due to its special distinguishing feature that its second variation retains its divergence-free property provided only the equations governing the static space-time and its linear perturbations are satisfied. When one seeks the corresponding flux integral for Einstein‒Maxwell space-times, the common procedure of including, together with the pseudo-tensor, the energy‒momentum tensor of the prevailing electromagnetic field fails. But, a prescription due to R. Sorkin, of including instead a suitably defined ‘Noether operator’, succeeds.

Exact solutions to Klein–Gordon and Weyl equations in a perfect-fluid Einstein–Maxwell space-time with local rotational symmetry

In this article we exhibit exact solutions of the Klein–Gordon and Weyl equations in a space-time homogeneous metric with local rotational symmetry, and the solutions of the Einstein–Maxwell equations with a perfect-fluid source and a sinusoidal electromagnetic configuration.

A conserved current for perturbations of Einstein-Maxwell space-times

Using the fact that the Einstein-Maxwell field equations arise from a Lagrangian variational principle, a closed 3-form associated with solutions of the perturbation equations is constructed. By dualizing with respect to the metric compatible volume element, a covariantly conserved current-known as the symplectic current - is obtained. A useful formula for the component of this current normal to a non-null hypersurface is found by ‘pulling back’ the 3-form to this hypersurface. This formula is then used to evaluate the symplectic current for axisymmetric, polar perturbations with harmonic time dependence of axisymmetric, static space-times. It is shown that this current reproduces the current found by Chandrasekhar & Ferrari.