New Models of General Relativistic Static Thick Disks
  New families of exact general relativistic thick disks are constructed using the ``displace, cut, fill and reflect'' method. A class of functions used to ``fill'' the disks is derived imposing conditions on the first and second derivatives to generate physically acceptable disks. The analysis of the function's curvature further restrict the ranges of the free parameters that allow phisically acceptable disks. Then this class of functions together with the Schwarzschild metric is employed to construct thick disks in isotropic, Weyl and Schwarzschild canonical coordinates. In these last coordinates an additional function must be added to one of the metric coefficients to generate exact disks. Disks in isotropic and Weyl coordinates satisfy all energy conditions, but those in Schwarzschild canonical coordinates do not satisfy the dominant energy condition. 
D. Vogt and P.S. Letelier