It is known that charged relativistic shear-free fluid spheres are described
by the equation yxx = f(x)y2+g(x)y3, where f and g are arbitrary functions
of x only and y is a function of x and an external parameter t.Necessary
and sufficient conditions on f and g are obtained such that this equation
possesses the Painlev´e property.In this case the general solution y is given
in terms of solutions of the first or second Painlev´e equation (or their autonomous
versions) and solutions of their linearizations.In the autonomous
case we recover the solutions of Wyman, Chatterjee, and Sussman and a large
class of (apparently new) solutions involving elliptic integrals of the second
kind.Solutions arising from the special Airy function solutions of the second
Painlev´e equation are also given.It is noted that, as in the neutral case, a
three-parameter family of choices of f and g are described by solutions of an
equation of Chazy type.
This is a pre-print. The definitive version: HALBURD, R., 2001. Solvable models of relativistic charged spherically symmetric fluids. Classical and Quantum Gravity, 18(1), pp. 11-25.