Tikekar superdense stars in electric fields

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.Comment: 15 pages, To appear in J. Math. Phy

A class of charged relativistic spheres

We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular parameter values it is possible to find solutions in terms of elementary functions. Our results contain models found previously for uncharged neutron stars and charged isotropic spheres.Comment: 11 pages, To appear in Mathematical and Computational Application

Analytical models for quark stars

We find two new classes of exact solutions to the Einstein-Maxwell system of equations. The matter content satisfies a linear equation of state consistent with quark matter; a particular form of one of the gravitational potentials is specified to generate solutions. The exact solutions can be written in terms of elementary functions, and these can be related to quark matter in the presence of an electromagnetic field. The first class of solutions generalises the Mak and Harko model. The second class of solutions does not admit any singularities in the matter and gravitational potentials at the centre.Comment: 10 pages, To appear in Int. J. Mod. Phys.