Solvable models of relativistic charged spherically symmetric fluids (Q2704290)

The Einstein-Maxwell equation for a shear-free non-rotating charged perfect fluid \(y''_{xx}(x, t)= f(x) y^2(x,t)+ g(x) y^3(x, t)\), where \(x= r^2\) and \(t\) is an external parameter, is studied concerning the behavior of arbitrary functions \(f(x)\) and \(g(x)\), for which necessary and sufficient conditions such that \(y(x, t)\) is a single-valued function of \(x\) (Painlevé property) are obtained. The general solution is given in terms of the first or second Painlevé equations, and their several versions. The autonomous and neutral cases are considered in detail.