Abstract:
To obtain an understanding of the gravitational dynamics of a general relativistic star
it is necessary to solve the Einstein-Maxwell equations. The matter distribution may
be isotropic in the presence of an electromagnetic field. The intention of this paper
is to provide a general framework that admits the possibility of a non-vanishing
electric field intensity. We believe that this approach will allow for a richer family
of solutions to the Einstein-Maxwell field equations and possibly provide a deeper
insight into the behavior of the gravitational field. We present a class of closed form solutions to the Einstein-Maxwell system of equations for static spherically
symmetric isotropic stars in the presence of an electric field by generalizing earlier
approaches. This is achieved by specifying a particular form for one of the
gravitational potentials and the electric field intensity. The solution of the system of
equations is reduced to a recurrence relation with variable, rational coefficients which
can be solved in general. Itis possible to expressed exact solutions in terms of integrals
form from the series solutions and the integral can be completed exactly for particular
parameter values. The physical features such as the gravitational potentials, electric
field intensity, charge distribution, and matter distribution are well behaved. These
exact solutions describe a charged relativistic sphere with isotropic pressures. Earlier
models can be contained in our general class of solutions. We can also obtain new exact
solutions from our general treatment which can be used to model a charged isotropic
relativistic sphere.
