Solvable models of relativistic charged spherically symmetric fluids

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.