An Interior model of Charged Fluid Spheres

TL;DR

The paper addresses the interior structure of charged fluid spheres within a spheroidal spacetime by employing the Vaidya–Tikekar metric and solving the Einstein–Maxwell equations. It prescribes an electric-field profile $E^2(r)$ to reduce the system to a hypergeometric differential equation for $e^{\nu/2}$, yielding a general solution in terms of ${}_2F_1$ and a physically viable closed-form for the special case $k=-23$. The main contributions include a new class of exact, physically acceptable charged fluid solutions, a computational scheme to determine mass $m$, radius $a$, and charge $q$ from boundary data, and a demonstration that the models satisfy hydrostatic equilibrium and standard energy conditions while matching smoothly to a Reissner–Nordström exterior. The work provides analytic interior models for ultra-dense charged matter and a framework for exploring mass-radius-charge relations of compact stars under charge, with potential implications for the structure of highly compact astrophysical objects.

Abstract

At constant time $t$, we examine the Vaidya-Tikekar metric characterising a three-dimensional, extremely dense spheroidal star configuration. The static, spherically symmetric solution of Einstein's field equations can be expressed in analytic closed form utilising a hypergeometric series. A relativistic, superdense state of matter at a constant $t$ is represented by the resultant model, which describes the geometry of a three-spheroid. Assuming a stellar density of $ρ_{a}= 2*10^{14} gm*cm^{-3}$, we investigate configurations whose total mass and radius vary over a range of well-defined values of the density variation parameter. Similar to an uncharged neutron star, all models possess the same total mass and boundary radius. The hypergeometric solution leads to a new class of exact, physically acceptable solutions. We show that the model satisfies the conditions of hydrostatic equilibrium and fulfils all standard energy conditions, which are verified throughout the analysis.

Figures (1)

• Figure 1: Always give a caption.