Tikekar superdense stars in electric fields

TL;DR

This paper derives new exact solutions to the Einstein-Maxwell equations for superdense stars with electric fields, generalizing previous models and explicitly relating spheroidal parameters to electromagnetic properties.

Contribution

It introduces a method to obtain exact solutions for charged spheroidal stellar models by solving a recurrence relation, extending previous uncharged models and explicitly linking spheroidal and electromagnetic parameters.

Findings

Derived new classes of solutions in elementary functions.

Generalized the Tikekar superdense star model to include electric charge.

Established a direct relationship between spheroidal parameter and electric field.

Abstract

We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface \{$t$ = constant\} are spheroidal. The solution of the Einstein-Maxwell system is reduced to a recurrence relation with variable rational coefficients which can be solved in general using mathematical induction. New classes of solutions of linearly independent functions are obtained by restricting the spheroidal parameter $K$ and the electric field intensity parameter $\alpha$. Consequently it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions. Our result contains models found previously including the superdense Tikekar neutron star model [R. Tikekar, \emph{J. Math. Phys.} \textbf{31}, 2454 (1990)] when $K=-7$ and $\alpha=0$. Our class of charged spheroidal models generalise the uncharged isotropic Maharaj and Leach solutions [S. D. Maharaj and P. G. L. Leach, \emph{J. Math. Phys.} \textbf{37}, 430 (1996)]. In particular, we find an explicit relationship directly relating the spheroidal parameter $K$ to the electromagnetic field.