  We present a general solution of the Einstein gravitational field equations
for the static spherically symmetric gravitational interior spacetime of an
isotropic fluid sphere. The solution is obtained by transforming the pressure
isotropy condition, a second order ordinary differential equation, into a
Riccati type first order differential equation, and using a general
integrability condition for the Riccati equation. This allows us to obtain an
exact non-singular solution of the interior field equations for a fluid sphere,
expressed in the form of infinite power series. The physical features of the
solution are studied in detail numerically by cutting the infinite series
expansions, and restricting our numerical analysis by taking into account only
$n=21$ terms in the power series representations of the relevant astrophysical
parameters. In the present model all physical quantities (density, pressure,
speed of sound etc.) are finite at the center of the sphere. The physical
behavior of the solution essentially depends on the equation of state of the
dense matter at the center of the star. The stability properties of the model
are also analyzed in detail for a number of central equations of state, and it
is shown that it is stable with respect to the radial adiabatic perturbations.
The astrophysical analysis indicates that this solution can be used as a
realistic model for static general relativistic high density objects, like
neutron stars.

General Relativity and Quantum Cosmology;Solar and Stellar Astrophysics;High Energy Physics - Theory