Solvable models of relativistic charged spherically symmetric fluids

Rod Halburd
2000 Classical and quantum gravity  
It is known that charged relativistic shear-free fluid spheres are described by the equation y xx = f (x)y 2 + g(x)y 3 , 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 Painlevé property. In this case the general solution y is given in terms of solutions of the first or second Painlevé equation (or their autonomous versions) and solutions of
more » ... nd 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 Painlevé 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.
doi:10.1088/0264-9381/18/1/302 fatcat:5wm7xoymv5gqlfke2mbitkecwi