## Models in isotropic coordinates with equation of state.

##### Abstract

In this thesis we consider spacetimes which are static and spherically symmetric related
to the Einstein and Einstein-Maxwell system of equations in isotropic coordinates. We
study both neutral and charged matter distributions with isotropic and anisotropic
pressures, respectively. Our aim is to model relativistic stellar models. A known
transformation that has been utilised by other researchers is applied to rewrite the
field equations in equivalent forms. We produce new models to the Einstein system
of equations with isotropic pressures by developing an algorithm that generates new
classes of exact solutions if a particular seed solution is known. By applying the
algorithm to the field equations and the condition of pressure isotropy we obtain a
nonlinear Bernoulli equation which can be integrated. We also consider charged matter
distributions with anisotropic pressures by introducing barotropic equations of state.
Both linear and quadratic equations of state are considered and new exact solutions
of the Einstein-Maxwell system are found. This is achieved by specifying a particular
form for one of the metric functions and the electric field intensity. We select particular
parameter values to regain the masses of known stars. For the linear equation of state
we regain masses of the stars PSR J1614-2230, Vela X-1, PSR J1903+327, 4U 1820-30
and SAX J1808.4-3658. The masses for the stars PSR J1614-2230, 4U 1608-52, PSR
J1903+327, EXO 1745-248 and SAX J1808.4-3658 are generated when a quadratic
equation of state is imposed. Extensive physical analyses for the stars PSR J1614-2230
and PSR J1903+327 indicate that our models are well behaved.