## Exact models of compact stars with equations of state.

##### Abstract

We study exact solutions to the Einstein-Maxwell system of equations and relate them to compact
objects. It is well known that there are substantial analytic difficulties in the modelling of
self-gravitating, static fluid spheres when the pressure explicitly depends on the matter density.
Much simplification in solving the Einstein-Maxwell equations is achieved with the introduction
of electric charge and anisotropic matter. In this thesis, in order to obtain analytical solutions,
we consider the general situation of anisotropy in the presence of electric charge satisfying a
barotropic equation of state. Firstly, a linear equation of state, secondly a quadratic equation
of state, and thirdly a polytropic equation of state are analysed. For each of these equations of
state the Einstein-Maxwell equations are integrated and exact solutions are found in terms of
elementary functions. By choosing specific rational forms for one of the gravitational potential
and particular forms for the electric charge, new classes of solutions in static spherically symmetric
interior spacetimes are generated in the presence of electric charge. It is interesting to
note that, from our new class of solutions with an equation of state, we can regain earlier models.
A detailed physical analysis performed indicates that the classes of solutions are physically reasonable.
We regain the current accurate observed masses for the binary pulsars PSR J1614-2230
, PSR J1903+327, Vela X-1, SMC X-1 and Cen X-3.