The generalized Roche model
  Some exact analytical formulas are presented for the generalized Roche model of rotating star. The gravitational field of the central core is described by the model of two equal-mass point centers placed symmetrically at rotation axis with the pure imaginary z coordinates. The all basic parameters of the critical figure of the rotating massless envelope are presented in analytical form. The existence of the concave form of the uniformly rotating liquid is shown for a large enough angular velocity of the rotation. 
Zakir F. Seidov