## Spherically symmetric charged Einstein-Maxwell solutions.

##### Abstract

In this thesis we study spherically symmetric spacetimes with a perfect fluid source
which incorporates charge. We seek explicit solutions to the Einstein- Maxwell system
of equations. For nonaccelerating spherically symmetric models a charged, dust
solution is found. With constant pressure the equations reduce to quadratures. Particular
solutions are also found, with no acceleration, with the equation of state
P =( y - 1)u. The Lie analysis is utilised to reduce the Einstein- Maxwell equations
to a syst.em of ordinary differential equations. The evolution of the model depends
on a Riccati equation for this general class of accelerating, expanding and shearing
spacetimes with charge. Also arbitrary choices for the gravitational potentials lead
to explicit solutions in particular cases. With constant gravitational potential A we
generate a simple nonvacuum model. The analysis, in this case, enables us to reduce
the solution to quadratures. With the value y = 2, for a stiff equation of state, we
find that the solution is expressable in terms of elementary functions. Throughout
the thesis we have attempted to relate our results to previously published work, and
to obtain the uncharged perfect fluid limit where appropriate.